LMFDB - Embedded newform 168.2.t.a.115.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(19,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.8
Character	$\chi$	$=$	168.115
Dual form			168.2.t.a.19.8

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.321935 - 1.37708i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.79272 + 0.886663i) q^{4} +(1.25150 + 2.16767i) q^{5} +(0.409738 - 1.35356i) q^{6} +(1.36321 + 2.26752i) q^{7} +(1.79815 + 2.18327i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.58215 - 2.42127i) q^{10} +(2.83809 - 4.91572i) q^{11} +(-1.99587 - 0.128485i) q^{12} -5.31228 q^{13} +(2.68370 - 2.60725i) q^{14} +2.50301i q^{15} +(2.42766 - 3.17907i) q^{16} +(-0.393919 - 0.227429i) q^{17} +(1.03162 - 0.967346i) q^{18} +(-3.19938 + 1.84716i) q^{19} +(-4.16558 - 2.77635i) q^{20} +(0.0468128 + 2.64534i) q^{21} +(-7.68304 - 2.32575i) q^{22} +(4.43443 - 2.56022i) q^{23} +(0.465606 + 2.78984i) q^{24} +(-0.632521 + 1.09556i) q^{25} +(1.71021 + 7.31545i) q^{26} +1.00000i q^{27} +(-4.45438 - 2.85632i) q^{28} -2.57962i q^{29} +(3.44685 - 0.805806i) q^{30} +(3.00333 - 5.20192i) q^{31} +(-5.15939 - 2.31963i) q^{32} +(4.91572 - 2.83809i) q^{33} +(-0.186372 + 0.615676i) q^{34} +(-3.20917 + 5.79280i) q^{35} +(-1.66423 - 1.10921i) q^{36} +(-7.80778 + 4.50782i) q^{37} +(3.57369 + 3.81115i) q^{38} +(-4.60057 - 2.65614i) q^{39} +(-2.48222 + 6.63015i) q^{40} +4.65692i q^{41} +(3.62778 - 0.916092i) q^{42} +3.66703 q^{43} +(-0.729306 + 11.3289i) q^{44} +(-1.25150 + 2.16767i) q^{45} +(-4.95323 - 5.28235i) q^{46} +(-0.478841 - 0.829377i) q^{47} +(3.69195 - 1.53933i) q^{48} +(-3.28332 + 6.18222i) q^{49} +(1.71230 + 0.518335i) q^{50} +(-0.227429 - 0.393919i) q^{51} +(9.52341 - 4.71020i) q^{52} +(-5.41124 - 3.12418i) q^{53} +(1.37708 - 0.321935i) q^{54} +14.2075 q^{55} +(-2.49936 + 7.05359i) q^{56} -3.69433 q^{57} +(-3.55235 + 0.830471i) q^{58} +(-8.76604 - 5.06108i) q^{59} +(-2.21932 - 4.48718i) q^{60} +(-2.50184 - 4.33331i) q^{61} +(-8.13036 - 2.46115i) q^{62} +(-1.28213 + 2.31434i) q^{63} +(-1.53334 + 7.85168i) q^{64} +(-6.64834 - 11.5153i) q^{65} +(-5.49083 - 5.85568i) q^{66} +(4.65133 - 8.05634i) q^{67} +(0.907837 + 0.0584425i) q^{68} +5.12043 q^{69} +(9.01031 + 2.55439i) q^{70} -7.35240i q^{71} +(-0.991694 + 2.64888i) q^{72} +(5.93541 + 3.42681i) q^{73} +(8.72125 + 9.30073i) q^{74} +(-1.09556 + 0.632521i) q^{75} +(4.09777 - 6.14821i) q^{76} +(15.0154 - 0.265718i) q^{77} +(-2.17664 + 7.19047i) q^{78} +(-7.71882 + 4.45646i) q^{79} +(9.92938 + 1.28374i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.41297 - 1.49923i) q^{82} +1.96259i q^{83} +(-2.42944 - 4.70083i) q^{84} -1.13851i q^{85} +(-1.18055 - 5.04980i) q^{86} +(1.28981 - 2.23402i) q^{87} +(15.8357 - 2.64286i) q^{88} +(5.91361 - 3.41423i) q^{89} +(3.38796 + 1.02558i) q^{90} +(-7.24175 - 12.0457i) q^{91} +(-5.67961 + 8.52158i) q^{92} +(5.20192 - 3.00333i) q^{93} +(-0.987965 + 0.926409i) q^{94} +(-8.00807 - 4.62346i) q^{95} +(-3.30835 - 4.58856i) q^{96} +3.71270i q^{97} +(9.57044 + 2.53113i) q^{98} +5.67619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.321935	−	1.37708i	−0.227643	−	0.973745i
$2$	−0.321935	−	1.37708i	−0.227643	−	0.973745i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.79272	+	0.886663i	−0.896358	+	0.443331i
$5$	1.25150	+	2.16767i	0.559689	+	0.969410i	0.997522	+	0.0703538i	$0.0224128\pi$
$5$	1.25150	+	2.16767i	0.559689	+	0.969410i	−0.437833	+	0.899056i	$0.644254\pi$
$6$	0.409738	−	1.35356i	0.167275	−	0.552587i
$7$	1.36321	+	2.26752i	0.515245	+	0.857043i
$7$	1.36321	+	2.26752i	0.515245	+	0.857043i
$8$	1.79815	+	2.18327i	0.635741	+	0.771903i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.58215	−	2.42127i	0.816549	−	0.765673i
$11$	2.83809	−	4.91572i	0.855717	−	1.48215i	−0.0202603	−	0.999795i	$-0.506450\pi$
$11$	2.83809	−	4.91572i	0.855717	−	1.48215i	0.875978	−	0.482351i	$-0.160217\pi$
$12$	−1.99587	−	0.128485i	−0.576158	−	0.0370905i
$13$	−5.31228			−1.47336			−0.736681	−	0.676241i	$-0.763608\pi$
$13$	−5.31228			−1.47336			−0.736681	+	0.676241i	$0.763608\pi$
$14$	2.68370	−	2.60725i	0.717250	−	0.696816i
$15$			2.50301i			0.646273i
$16$	2.42766	−	3.17907i	0.606914	−	0.794767i
$17$	−0.393919	−	0.227429i	−0.0955393	−	0.0551596i	0.451469	−	0.892287i	$-0.350900\pi$
$17$	−0.393919	−	0.227429i	−0.0955393	−	0.0551596i	−0.547008	+	0.837127i	$0.684233\pi$
$18$	1.03162	−	0.967346i	0.243155	−	0.228006i
$19$	−3.19938	+	1.84716i	−0.733988	+	0.423768i	−0.819879	−	0.572536i	$-0.805960\pi$
$19$	−3.19938	+	1.84716i	−0.733988	+	0.423768i	0.0858912	+	0.996305i	$0.472626\pi$
$20$	−4.16558	−	2.77635i	−0.931452	−	0.620811i
$21$	0.0468128	+	2.64534i	0.0102154	+	0.577260i
$22$	−7.68304	−	2.32575i	−1.63803	−	0.495851i
$23$	4.43443	−	2.56022i	0.924642	−	0.533842i	0.0395287	−	0.999218i	$-0.487414\pi$
$23$	4.43443	−	2.56022i	0.924642	−	0.533842i	0.885113	+	0.465376i	$0.154081\pi$
$24$	0.465606	+	2.78984i	0.0950413	+	0.569474i
$25$	−0.632521	+	1.09556i	−0.126504	+	0.219112i
$26$	1.71021	+	7.31545i	0.335400	+	1.43468i
$27$			1.00000i			0.192450i
$28$	−4.45438	−	2.85632i	−0.841798	−	0.539793i
$29$		−	2.57962i		−	0.479024i	−0.970893	−	0.239512i	$-0.923013\pi$
$29$		−	2.57962i		−	0.479024i	0.970893	−	0.239512i	$-0.0769874\pi$
$30$	3.44685	−	0.805806i	0.629305	−	0.147119i
$31$	3.00333	−	5.20192i	0.539414	−	0.934293i	−0.459521	−	0.888167i	$-0.651979\pi$
$31$	3.00333	−	5.20192i	0.539414	−	0.934293i	0.998936	−	0.0461260i	$-0.0146876\pi$
$32$	−5.15939	−	2.31963i	−0.912060	−	0.410057i
$33$	4.91572	−	2.83809i	0.855717	−	0.494049i
$34$	−0.186372	+	0.615676i	−0.0319626	+	0.105588i
$35$	−3.20917	+	5.79280i	−0.542449	+	0.979161i
$36$	−1.66423	−	1.10921i	−0.277372	−	0.184868i
$37$	−7.80778	+	4.50782i	−1.28359	+	0.741082i	−0.977503	−	0.210922i	$-0.932354\pi$
$37$	−7.80778	+	4.50782i	−1.28359	+	0.741082i	−0.306088	+	0.952003i	$0.599020\pi$
$38$	3.57369	+	3.81115i	0.579729	+	0.618250i
$39$	−4.60057	−	2.65614i	−0.736681	−	0.425323i
$40$	−2.48222	+	6.63015i	−0.392473	+	1.04832i
$41$			4.65692i			0.727289i	0.931538	+	0.363644i	$0.118468\pi$
$41$			4.65692i			0.727289i	−0.931538	+	0.363644i	$0.881532\pi$
$42$	3.62778	−	0.916092i	0.559778	−	0.141356i
$43$	3.66703			0.559217			0.279608	−	0.960114i	$-0.409795\pi$
$43$	3.66703			0.559217			0.279608	+	0.960114i	$0.409795\pi$
$44$	−0.729306	+	11.3289i	−0.109947	+	1.70790i
$45$	−1.25150	+	2.16767i	−0.186563	+	0.323137i
$46$	−4.95323	−	5.28235i	−0.730314	−	0.778840i
$47$	−0.478841	−	0.829377i	−0.0698461	−	0.120977i	0.828987	−	0.559267i	$-0.188918\pi$
$47$	−0.478841	−	0.829377i	−0.0698461	−	0.120977i	−0.898833	+	0.438290i	$0.855584\pi$
$48$	3.69195	−	1.53933i	0.532887	−	0.222182i
$49$	−3.28332	+	6.18222i	−0.469046	+	0.883174i
$50$	1.71230	+	0.518335i	0.242156	+	0.0733036i
$51$	−0.227429	−	0.393919i	−0.0318464	−	0.0551596i
$52$	9.52341	−	4.71020i	1.32066	−	0.653188i
$53$	−5.41124	−	3.12418i	−0.743290	−	0.429139i	0.0799741	−	0.996797i	$-0.474516\pi$
$53$	−5.41124	−	3.12418i	−0.743290	−	0.429139i	−0.823264	+	0.567658i	$0.807850\pi$
$54$	1.37708	−	0.321935i	0.187397	−	0.0438098i
$55$	14.2075			1.91574
$56$	−2.49936	+	7.05359i	−0.333992	+	0.942576i
$57$	−3.69433			−0.489326
$58$	−3.55235	+	0.830471i	−0.466447	+	0.109046i
$59$	−8.76604	−	5.06108i	−1.14124	−	0.658896i	−0.194503	−	0.980902i	$-0.562310\pi$
$59$	−8.76604	−	5.06108i	−1.14124	−	0.658896i	−0.946738	+	0.322006i	$0.895643\pi$
$60$	−2.21932	−	4.48718i	−0.286513	−	0.579292i
$61$	−2.50184	−	4.33331i	−0.320327	−	0.554823i	0.660228	−	0.751065i	$-0.270460\pi$
$61$	−2.50184	−	4.33331i	−0.320327	−	0.554823i	−0.980555	+	0.196242i	$0.937126\pi$
$62$	−8.13036	−	2.46115i	−1.03256	−	0.312567i
$63$	−1.28213	+	2.31434i	−0.161533	+	0.291579i
$64$	−1.53334	+	7.85168i	−0.191667	+	0.981460i
$65$	−6.64834	−	11.5153i	−0.824625	−	1.42829i
$66$	−5.49083	−	5.85568i	−0.675875	−	0.720784i
$67$	4.65133	−	8.05634i	0.568251	−	0.984239i	−0.428489	−	0.903547i	$-0.640954\pi$
$67$	4.65133	−	8.05634i	0.568251	−	0.984239i	0.996739	−	0.0806916i	$-0.0257129\pi$
$68$	0.907837	+	0.0584425i	0.110091	+	0.00708720i
$69$	5.12043			0.616428
$70$	9.01031	+	2.55439i	1.07694	+	0.305308i
$71$		−	7.35240i		−	0.872569i	−0.899809	−	0.436285i	$-0.856294\pi$
$71$		−	7.35240i		−	0.872569i	0.899809	−	0.436285i	$-0.143706\pi$
$72$	−0.991694	+	2.64888i	−0.116872	+	0.312173i
$73$	5.93541	+	3.42681i	0.694687	+	0.401078i	0.805366	−	0.592779i	$-0.201969\pi$
$73$	5.93541	+	3.42681i	0.694687	+	0.401078i	−0.110678	+	0.993856i	$0.535302\pi$
$74$	8.72125	+	9.30073i	1.01382	+	1.08119i
$75$	−1.09556	+	0.632521i	−0.126504	+	0.0730372i
$76$	4.09777	−	6.14821i	0.470046	−	0.705248i
$77$	15.0154	−	0.265718i	1.71117	−	0.0302814i
$78$	−2.17664	+	7.19047i	−0.246456	+	0.814161i
$79$	−7.71882	+	4.45646i	−0.868435	+	0.501391i	−0.866828	−	0.498607i	$-0.833845\pi$
$79$	−7.71882	+	4.45646i	−0.868435	+	0.501391i	−0.00160740	+	0.999999i	$0.500512\pi$
$80$	9.92938	+	1.28374i	1.11014	+	0.143526i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.41297	−	1.49923i	0.708194	−	0.165562i
$83$			1.96259i			0.215423i	0.994182	+	0.107711i	$0.0343522\pi$
$83$			1.96259i			0.215423i	−0.994182	+	0.107711i	$0.965648\pi$
$84$	−2.42944	−	4.70083i	−0.265074	−	0.512903i
$85$		−	1.13851i		−	0.123489i
$86$	−1.18055	−	5.04980i	−0.127302	−	0.544534i
$87$	1.28981	−	2.23402i	0.138282	−	0.239512i
$88$	15.8357	−	2.64286i	1.68809	−	0.281730i
$89$	5.91361	−	3.41423i	0.626842	−	0.361907i	−0.152686	−	0.988275i	$-0.548792\pi$
$89$	5.91361	−	3.41423i	0.626842	−	0.361907i	0.779528	+	0.626367i	$0.215459\pi$
$90$	3.38796	+	1.02558i	0.357122	+	0.108105i
$91$	−7.24175	−	12.0457i	−0.759142	−	1.26273i
$92$	−5.67961	+	8.52158i	−0.592141	+	0.888436i
$93$	5.20192	−	3.00333i	0.539414	−	0.311431i
$94$	−0.987965	+	0.926409i	−0.101901	+	0.0955518i
$95$	−8.00807	−	4.62346i	−0.821611	−	0.474357i
$96$	−3.30835	−	4.58856i	−0.337657	−	0.468318i
$97$			3.71270i			0.376967i	0.982076	+	0.188484i	$0.0603573\pi$
$97$			3.71270i			0.376967i	−0.982076	+	0.188484i	$0.939643\pi$
$98$	9.57044	+	2.53113i	0.966761	+	0.255683i
$99$	5.67619			0.570478
$100$	0.162539	−	2.52486i	0.0162539	−	0.252486i
$101$	2.84077	−	4.92036i	0.282667	−	0.489594i	−0.689373	−	0.724406i	$-0.742114\pi$
$101$	2.84077	−	4.92036i	0.282667	−	0.489594i	0.972041	+	0.234812i	$0.0754474\pi$
$102$	−0.469241	+	0.440005i	−0.0464618	+	0.0435670i
$103$	2.95345	+	5.11553i	0.291013	+	0.504049i	0.974049	−	0.226335i	$-0.0726745\pi$
$103$	2.95345	+	5.11553i	0.291013	+	0.504049i	−0.683037	+	0.730384i	$0.739341\pi$
$104$	−9.55226	−	11.5981i	−0.936676	−	1.13729i
$105$	−5.67562	+	3.41212i	−0.553884	+	0.332989i
$106$	−2.56019	+	8.45750i	−0.248667	+	0.821465i
$107$	5.33045	+	9.23261i	0.515314	+	0.892550i	0.999842	+	0.0177741i	$0.00565795\pi$
$107$	5.33045	+	9.23261i	0.515314	+	0.892550i	−0.484528	+	0.874776i	$0.661009\pi$
$108$	−0.886663	−	1.79272i	−0.0853192	−	0.172504i
$109$	2.75319	+	1.58956i	0.263708	+	0.152252i	0.626025	−	0.779803i	$-0.284681\pi$
$109$	2.75319	+	1.58956i	0.263708	+	0.152252i	−0.362317	+	0.932055i	$0.618014\pi$
$110$	−4.57390	−	19.5650i	−0.436105	−	1.86545i
$111$	−9.01565			−0.855727
$112$	10.5180	+	1.17103i	0.993859	+	0.110652i
$113$	−0.302446			−0.0284518			−0.0142259	−	0.999899i	$-0.504528\pi$
$113$	−0.302446			−0.0284518			−0.0142259	+	0.999899i	$0.504528\pi$
$114$	1.18933	+	5.08739i	0.111391	+	0.476478i
$115$	11.0994	+	6.40824i	1.03502	+	0.597571i
$116$	2.28726	+	4.62453i	0.212366	+	0.429377i
$117$	−2.65614	−	4.60057i	−0.245560	−	0.425323i
$118$	−4.14742	+	13.7009i	−0.381801	+	1.26127i
$119$	−0.0212932	−	1.20325i	−0.00195194	−	0.110302i
$120$	−5.46474	+	4.50077i	−0.498860	+	0.410862i
$121$	−10.6096	−	18.3763i	−0.964505	−	1.67057i
$122$	−5.16189	+	4.84028i	−0.467336	+	0.438218i
$123$	−2.32846	+	4.03301i	−0.209950	+	0.363644i
$124$	−0.771767	+	11.9885i	−0.0693067	+	1.07660i
$125$	9.34863			0.836167
$126$	3.59979	+	1.02053i	0.320695	+	0.0909160i
$127$			6.39751i			0.567687i	0.958871	+	0.283843i	$0.0916096\pi$
$127$			6.39751i			0.567687i	−0.958871	+	0.283843i	$0.908390\pi$
$128$	11.3061	−	0.416198i	0.999323	−	0.0367871i
$129$	3.17574	+	1.83351i	0.279608	+	0.161432i
$130$	−13.7171	+	12.8625i	−1.20307	+	1.12811i
$131$	−12.5596	+	7.25130i	−1.09734	+	0.633549i	−0.935521	−	0.353272i	$-0.885069\pi$
$131$	−12.5596	+	7.25130i	−1.09734	+	0.633549i	−0.161818	+	0.986821i	$0.551736\pi$
$132$	−6.29606	+	9.44648i	−0.548002	+	0.822211i
$133$	−8.54991	−	4.73660i	−0.741371	−	0.410715i
$134$	−12.5917	−	3.81165i	−1.08776	−	0.329276i
$135$	−2.16767	+	1.25150i	−0.186563	+	0.107712i
$136$	−0.211784	−	1.26898i	−0.0181604	−	0.108814i
$137$	−0.615559	+	1.06618i	−0.0525908	+	0.0910899i	−0.891122	−	0.453763i	$-0.850081\pi$
$137$	−0.615559	+	1.06618i	−0.0525908	+	0.0910899i	0.838532	+	0.544853i	$0.183415\pi$
$138$	−1.64845	−	7.05126i	−0.140325	−	0.600243i
$139$			15.7788i			1.33834i	0.743108	+	0.669172i	$0.233351\pi$
$139$			15.7788i			1.33834i	−0.743108	+	0.669172i	$0.766649\pi$
$140$	0.616877	−	13.2303i	0.0521356	−	1.11816i
$141$		−	0.957682i		−	0.0806514i
$142$	−10.1249	+	2.36700i	−0.849660	+	0.198634i
$143$	−15.0768	+	26.1137i	−1.26078	+	2.18374i
$144$	3.96698	+	0.512879i	0.330582	+	0.0427399i
$145$	5.59176	−	3.22841i	0.464371	−	0.268104i
$146$	2.80819	−	9.27676i	0.232407	−	0.767750i
$147$	−5.93455	+	3.71230i	−0.489473	+	0.306185i
$148$	10.0002	−	15.0041i	0.822012	−	1.23333i
$149$	−5.15767	+	2.97778i	−0.422532	+	0.243949i	−0.696160	−	0.717886i	$-0.745110\pi$
$149$	−5.15767	+	2.97778i	−0.422532	+	0.243949i	0.273628	+	0.961836i	$0.411776\pi$
$150$	1.22373	+	1.30504i	0.0999173	+	0.106556i
$151$	3.11126	+	1.79629i	0.253191	+	0.146180i	0.621224	−	0.783633i	$-0.286636\pi$
$151$	3.11126	+	1.79629i	0.253191	+	0.146180i	−0.368034	+	0.929812i	$0.619969\pi$
$152$	−9.78581	−	3.66364i	−0.793734	−	0.297161i
$153$		−	0.454858i		−	0.0367731i
$154$	−5.19991	−	20.5920i	−0.419021	−	1.65935i
$155$	15.0347			1.20762
$156$	10.6026	+	0.682549i	0.848889	+	0.0546477i
$157$	−0.491762	+	0.851757i	−0.0392469	+	0.0679776i	−0.884982	−	0.465626i	$-0.845829\pi$
$157$	−0.491762	+	0.851757i	−0.0392469	+	0.0679776i	0.845735	+	0.533604i	$0.179163\pi$
$158$	8.62188	+	9.19477i	0.685920	+	0.731496i
$159$	−3.12418	−	5.41124i	−0.247763	−	0.429139i
$160$	−1.42880	−	14.0869i	−0.112957	−	1.11366i
$161$	11.8504	+	6.56505i	0.933942	+	0.517398i
$162$	1.35356	+	0.409738i	0.106345	+	0.0321920i
$163$	−1.26083	−	2.18383i	−0.0987562	−	0.171051i	0.812414	−	0.583081i	$-0.198153\pi$
$163$	−1.26083	−	2.18383i	−0.0987562	−	0.171051i	−0.911170	+	0.412030i	$0.864820\pi$
$164$	−4.12912	−	8.34854i	−0.322430	−	0.651911i
$165$	12.3041	+	7.10377i	0.957872	+	0.553028i
$166$	2.70266	−	0.631828i	0.209767	−	0.0490394i
$167$	−5.26232			−0.407211			−0.203605	−	0.979053i	$-0.565266\pi$
$167$	−5.26232			−0.407211			−0.203605	+	0.979053i	$0.565266\pi$
$168$	−5.69131	+	4.85891i	−0.439094	+	0.374873i
$169$	15.2203			1.17079
$170$	−1.56783	+	0.366527i	−0.120247	+	0.0281114i
$171$	−3.19938	−	1.84716i	−0.244663	−	0.141256i
$172$	−6.57394	+	3.25142i	−0.501258	+	0.247918i
$173$	−0.0718117	−	0.124381i	−0.00545974	−	0.00945654i	0.863283	−	0.504721i	$-0.168405\pi$
$173$	−0.0718117	−	0.124381i	−0.00545974	−	0.00945654i	−0.868742	+	0.495264i	$0.835071\pi$
$174$	−3.49166	−	1.05697i	−0.264702	−	0.0801285i
$175$	−3.34646	+	0.0592202i	−0.252969	+	0.00447662i
$176$	−8.73750	−	20.9562i	−0.658614	−	1.57963i
$177$	−5.06108	−	8.76604i	−0.380414	−	0.658896i
$178$	−6.60547	−	7.04438i	−0.495101	−	0.527998i
$179$	9.46239	−	16.3893i	0.707252	−	1.22500i	−0.258621	−	0.965979i	$-0.583268\pi$
$179$	9.46239	−	16.3893i	0.707252	−	1.22500i	0.965873	−	0.259018i	$-0.0833987\pi$
$180$	0.321599	−	4.99567i	0.0239706	−	0.372355i
$181$	22.2260			1.65204			0.826022	−	0.563637i	$-0.190598\pi$
$181$	22.2260			1.65204			0.826022	+	0.563637i	$0.190598\pi$
$182$	−14.2566	+	13.8504i	−1.05677	+	1.02666i
$183$		−	5.00367i		−	0.369882i
$184$	13.5634	+	5.07790i	0.999906	+	0.374348i
$185$	−19.5429	−	11.2831i	−1.43682	−	0.829551i
$186$	−5.81052	−	6.19660i	−0.426048	−	0.454357i
$187$	−2.23596	+	1.29093i	−0.163509	+	0.0944021i
$188$	1.59380	+	1.06227i	0.116240	+	0.0774737i
$189$	−2.26752	+	1.36321i	−0.164938	+	0.0991589i
$190$	−3.78881	+	12.5162i	−0.274869	+	0.908023i
$191$	−10.2112	+	5.89547i	−0.738860	+	0.426581i	−0.821655	−	0.569986i	$-0.806949\pi$
$191$	−10.2112	+	5.89547i	−0.738860	+	0.426581i	0.0827947	+	0.996567i	$0.473615\pi$
$192$	−5.25375	+	6.03309i	−0.379157	+	0.435400i
$193$	−13.4112	+	23.2289i	−0.965361	+	1.67205i	−0.256719	+	0.966486i	$0.582641\pi$
$193$	−13.4112	+	23.2289i	−0.965361	+	1.67205i	−0.708642	+	0.705568i	$0.750692\pi$
$194$	5.11270	−	1.19525i	0.367070	−	0.0858138i
$195$		−	13.2967i		−	0.952195i
$196$	0.404513	−	13.9942i	0.0288938	−	0.999582i
$197$			16.5842i			1.18157i	0.806828	+	0.590786i	$0.201182\pi$
$197$			16.5842i			1.18157i	−0.806828	+	0.590786i	$0.798818\pi$
$198$	−1.82736	−	7.81658i	−0.129865	−	0.555500i
$199$	5.70420	−	9.87996i	0.404360	−	0.700372i	−0.589887	−	0.807486i	$-0.700828\pi$
$199$	5.70420	−	9.87996i	0.404360	−	0.700372i	0.994247	+	0.107114i	$0.0341610\pi$
$200$	−3.52926	+	0.589010i	−0.249557	+	0.0416493i
$201$	8.05634	−	4.65133i	0.568251	−	0.328080i
$202$	−7.69029	−	2.32794i	−0.541087	−	0.163793i
$203$	5.84935	−	3.51657i	0.410544	−	0.246815i
$204$	0.756989	+	0.504531i	0.0529998	+	0.0353242i
$205$	−10.0947	+	5.82815i	−0.705041	+	0.407056i
$206$	6.09369	−	5.71402i	0.424568	−	0.398115i
$207$	4.43443	+	2.56022i	0.308214	+	0.177947i
$208$	−12.8964	+	16.8881i	−0.894205	+	1.17098i
$209$			20.9697i			1.45050i
$210$	6.52596	+	6.71732i	0.450334	+	0.463539i
$211$	−4.13300			−0.284527			−0.142264	−	0.989829i	$-0.545438\pi$
$211$	−4.13300			−0.284527			−0.142264	+	0.989829i	$0.545438\pi$
$212$	12.4709	+	0.802821i	0.856505	+	0.0551380i
$213$	3.67620	−	6.36736i	0.251889	−	0.436285i
$214$	10.9980	−	10.3128i	0.751808	−	0.704966i
$215$	4.58930	+	7.94890i	0.312988	+	0.542110i
$216$	−2.18327	+	1.79815i	−0.148553	+	0.122348i
$217$	15.8896	−	0.281189i	1.07866	−	0.0190883i
$218$	1.30260	−	4.30311i	0.0882233	−	0.291443i
$219$	3.42681	+	5.93541i	0.231562	+	0.401078i
$220$	−25.4701	+	12.5973i	−1.71719	+	0.849309i
$221$	2.09261	+	1.20817i	0.140764	+	0.0812701i
$222$	2.90245	+	12.4153i	0.194800	+	0.833260i
$223$	−18.1063			−1.21249			−0.606245	−	0.795278i	$-0.707325\pi$
$223$	−18.1063			−1.21249			−0.606245	+	0.795278i	$0.707325\pi$
$224$	−1.77351	−	14.8612i	−0.118498	−	0.992954i
$225$	−1.26504			−0.0843361
$226$	0.0973682	+	0.416494i	0.00647683	+	0.0277048i
$227$	6.86343	+	3.96260i	0.455542	+	0.263007i	0.710168	−	0.704032i	$-0.248619\pi$
$227$	6.86343	+	3.96260i	0.455542	+	0.263007i	−0.254626	+	0.967040i	$0.581952\pi$
$228$	6.62288	−	3.27562i	0.438611	−	0.216933i
$229$	1.07787	+	1.86692i	0.0712274	+	0.123370i	0.899440	−	0.437045i	$-0.143975\pi$
$229$	1.07787	+	1.86692i	0.0712274	+	0.123370i	−0.828212	+	0.560415i	$0.810642\pi$
$230$	5.25139	−	17.3478i	0.346266	−	1.14388i
$231$	13.1366	+	7.27760i	0.864325	+	0.478831i
$232$	5.63201	−	4.63854i	0.369760	−	0.304535i
$233$	10.0072	+	17.3330i	0.655594	+	1.13552i	0.981745	+	0.190204i	$0.0609149\pi$
$233$	10.0072	+	17.3330i	0.655594	+	1.13552i	−0.326151	+	0.945318i	$0.605752\pi$
$234$	−5.48026	+	5.13881i	−0.358256	+	0.335935i
$235$	1.19854	−	2.07594i	0.0781843	−	0.135419i
$236$	20.2025	+	1.30055i	1.31507	+	0.0846583i
$237$	−8.91293			−0.578957
$238$	−1.65012	+	0.416692i	−0.106962	+	0.0270101i
$239$		−	18.8923i		−	1.22204i	−0.791614	−	0.611021i	$-0.790759\pi$
$239$		−	18.8923i		−	1.22204i	0.791614	−	0.611021i	$-0.209241\pi$
$240$	7.95723	+	6.07644i	0.513637	+	0.392233i
$241$	−15.8555	−	9.15417i	−1.02134	−	0.589672i	−0.106849	−	0.994275i	$-0.534076\pi$
$241$	−15.8555	−	9.15417i	−1.02134	−	0.589672i	−0.914492	+	0.404603i	$0.867410\pi$
$242$	−21.8901	+	20.5262i	−1.40715	+	1.31947i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	8.32726	+	5.55010i	0.533098	+	0.355309i
$245$	−17.5101	+	0.619923i	−1.11868	+	0.0396054i
$246$	6.30341	+	1.90812i	0.401890	+	0.121657i
$247$	16.9960	−	9.81265i	1.08143	−	0.624364i
$248$	16.7576	−	2.79673i	1.06411	−	0.177593i
$249$	−0.981297	+	1.69966i	−0.0621872	+	0.107711i
$250$	−3.00965	−	12.8738i	−0.190347	−	0.814213i
$251$			3.43251i			0.216658i	0.994115	+	0.108329i	$0.0345500\pi$
$251$			3.43251i			0.216658i	−0.994115	+	0.108329i	$0.965450\pi$
$252$	0.246454	−	5.28576i	0.0155252	−	0.332972i
$253$		−	29.0645i		−	1.82727i
$254$	8.80990	−	2.05958i	0.552782	−	0.129230i
$255$	0.569256	−	0.985981i	0.0356482	−	0.0617445i
$256$	−4.21295	−	15.4354i	−0.263310	−	0.964711i
$257$	21.7104	−	12.5345i	1.35426	−	0.781882i	0.365417	−	0.930844i	$-0.380927\pi$
$257$	21.7104	−	12.5345i	1.35426	−	0.781882i	0.988843	+	0.148962i	$0.0475932\pi$
$258$	1.50252	−	4.96353i	0.0935428	−	0.309016i
$259$	−20.8652	−	11.5592i	−1.29650	−	0.718254i
$260$	22.1287	+	14.7487i	1.37237	+	0.914678i
$261$	2.23402	−	1.28981i	0.138282	−	0.0798373i
$262$	14.0290	+	14.9612i	0.866716	+	0.924305i
$263$	13.4314	+	7.75460i	0.828214	+	0.478169i	0.853241	−	0.521517i	$-0.174634\pi$
$263$	13.4314	+	7.75460i	0.828214	+	0.478169i	−0.0250270	+	0.999687i	$0.507967\pi$
$264$	15.0355	+	5.62904i	0.925372	+	0.346444i
$265$		−	15.6397i		−	0.960738i
$266$	−3.77017	+	13.2988i	−0.231164	+	0.815403i
$267$	6.82845			0.417894
$268$	−1.19525	+	18.5669i	−0.0730118	+	1.13415i
$269$	−11.8667	+	20.5537i	−0.723523	+	1.25318i	0.236055	+	0.971740i	$0.424145\pi$
$269$	−11.8667	+	20.5537i	−0.723523	+	1.25318i	−0.959579	+	0.281440i	$0.909188\pi$
$270$	2.42127	+	2.58215i	0.147354	+	0.157145i
$271$	7.35684	+	12.7424i	0.446896	+	0.774047i	0.998182	−	0.0602693i	$-0.0191959\pi$
$271$	7.35684	+	12.7424i	0.446896	+	0.774047i	−0.551286	+	0.834316i	$0.685863\pi$
$272$	−1.67931	+	0.700175i	−0.101823	+	0.0424543i
$273$	−0.248683	−	14.0528i	−0.0150510	−	0.850513i
$274$	1.66639	+	0.504436i	0.100670	+	0.0304741i
$275$	3.59031	+	6.21859i	0.216504	+	0.374995i
$276$	−9.17948	+	4.54010i	−0.552540	+	0.273282i
$277$	6.16822	+	3.56123i	0.370613	+	0.213973i	0.673726	−	0.738981i	$-0.264693\pi$
$277$	6.16822	+	3.56123i	0.370613	+	0.213973i	−0.303113	+	0.952954i	$0.598026\pi$
$278$	21.7288	−	5.07976i	1.30321	−	0.304664i
$279$	6.00666			0.359609
$280$	−18.4178	+	3.40981i	−1.10067	+	0.203775i
$281$	−13.0561			−0.778861			−0.389430	−	0.921056i	$-0.627328\pi$
$281$	−13.0561			−0.778861			−0.389430	+	0.921056i	$0.627328\pi$
$282$	−1.31881	+	0.308312i	−0.0785339	+	0.0183597i
$283$	−1.83051	−	1.05685i	−0.108813	−	0.0628230i	0.444606	−	0.895726i	$-0.353344\pi$
$283$	−1.83051	−	1.05685i	−0.108813	−	0.0628230i	−0.553419	+	0.832903i	$0.686677\pi$
$284$	6.51910	+	13.1808i	0.386837	+	0.782134i
$285$	−4.62346	−	8.00807i	−0.273870	−	0.474357i
$286$	40.8145	+	12.3550i	2.41341	+	0.730568i
$287$	−10.5597	+	6.34836i	−0.623318	+	0.374732i
$288$	−0.570834	−	5.62798i	−0.0336367	−	0.331632i
$289$	−8.39655	−	14.5433i	−0.493915	−	0.855486i
$290$	−6.24597	−	6.66098i	−0.366776	−	0.391146i
$291$	−1.85635	+	3.21529i	−0.108821	+	0.188484i
$292$	−13.6789	−	0.880589i	−0.800498	−	0.0515325i
$293$	0.334002			0.0195126			0.00975630	−	0.999952i	$-0.496894\pi$
$293$	0.334002			0.0195126			0.00975630	+	0.999952i	$0.496894\pi$
$294$	7.02268	+	6.97724i	0.409571	+	0.406921i
$295$		−	25.3358i		−	1.47511i
$296$	−23.8813	−	8.94077i	−1.38807	−	0.519671i
$297$	4.91572	+	2.83809i	0.285239	+	0.164683i
$298$	5.76108	+	6.14388i	0.333731	+	0.355906i
$299$	−23.5569	+	13.6006i	−1.36233	+	0.786542i
$300$	1.40319	−	2.10532i	0.0810133	−	0.121551i
$301$	4.99893	+	8.31507i	0.288134	+	0.479273i
$302$	1.47201	−	4.86275i	0.0847047	−	0.279820i
$303$	4.92036	−	2.84077i	0.282667	−	0.163198i
$304$	−1.89474	+	14.6553i	−0.108671	+	0.840541i
$305$	6.26211	−	10.8463i	0.358567	−	0.621057i
$306$	−0.626377	+	0.146435i	−0.0358076	+	0.00837112i
$307$		−	9.39141i		−	0.535996i	−0.963419	−	0.267998i	$-0.913638\pi$
$307$		−	9.39141i		−	0.535996i	0.963419	−	0.267998i	$-0.0863621\pi$
$308$	−26.6828	+	13.7900i	−1.52039	+	0.785757i
$309$			5.90691i			0.336032i
$310$	−4.84020	−	20.7040i	−0.274905	−	1.17591i
$311$	7.93750	−	13.7482i	0.450095	−	0.779587i	−0.548297	−	0.836284i	$-0.684724\pi$
$311$	7.93750	−	13.7482i	0.450095	−	0.779587i	0.998391	+	0.0566971i	$0.0180569\pi$
$312$	−2.47343	−	14.8204i	−0.140030	−	0.839041i
$313$	−27.8562	+	16.0828i	−1.57453	+	0.909054i	−0.578924	+	0.815381i	$0.696527\pi$
$313$	−27.8562	+	16.0828i	−1.57453	+	0.909054i	−0.995603	+	0.0936727i	$0.970139\pi$
$314$	1.33125	+	0.402987i	0.0751271	+	0.0227418i
$315$	−6.62130	+	0.117173i	−0.373068	+	0.00660194i
$316$	9.88627	−	14.8332i	0.556146	−	0.834431i
$317$	13.2252	−	7.63558i	0.742802	−	0.428857i	−0.0802854	−	0.996772i	$-0.525583\pi$
$317$	13.2252	−	7.63558i	0.742802	−	0.428857i	0.823087	+	0.567915i	$0.192250\pi$
$318$	−6.44594	+	6.04432i	−0.361470	+	0.338949i
$319$	−12.6807	−	7.32121i	−0.709983	−	0.409909i
$320$	−18.9388	+	6.50264i	−1.05871	+	0.363508i
$321$			10.6609i			0.595033i
$322$	5.22556	−	18.4325i	0.291209	−	1.02720i
$323$	1.68039			0.0934996
$324$	0.128485	−	1.99587i	0.00713807	−	0.110882i
$325$	3.36013	−	5.81991i	0.186386	−	0.322831i
$326$	−2.60141	+	2.43933i	−0.144079	+	0.135102i
$327$	1.58956	+	2.75319i	0.0879027	+	0.152252i
$328$	−10.1673	+	8.37383i	−0.561396	+	0.462367i
$329$	1.22787	−	2.21640i	0.0676947	−	0.122194i
$330$	5.82136	−	19.2307i	0.320455	−	1.05862i
$331$	10.5189	+	18.2193i	0.578174	+	1.00143i	0.995689	+	0.0927561i	$0.0295677\pi$
$331$	10.5189	+	18.2193i	0.578174	+	1.00143i	−0.417515	+	0.908670i	$0.637099\pi$
$332$	−1.74016	−	3.51837i	−0.0955037	−	0.193096i
$333$	−7.80778	−	4.50782i	−0.427864	−	0.247027i
$334$	1.69413	+	7.24665i	0.0926984	+	0.396519i
$335$	23.2846			1.27217
$336$	8.52335	+	6.27315i	0.464987	+	0.342229i
$337$	1.18351			0.0644697			0.0322348	−	0.999480i	$-0.489738\pi$
$337$	1.18351			0.0644697			0.0322348	+	0.999480i	$0.489738\pi$
$338$	−4.89996	−	20.9597i	−0.266523	−	1.14006i
$339$	−0.261926	−	0.151223i	−0.0142259	−	0.00821332i
$340$	1.00948	+	2.04103i	0.0547466	+	0.110690i
$341$	−17.0475	−	29.5271i	−0.923172	−	1.59898i
$342$	−1.51370	+	5.00048i	−0.0818517	+	0.270395i
$343$	−18.4942	+	0.982659i	−0.998591	+	0.0530586i
$344$	6.59386	+	8.00612i	0.355517	+	0.431661i
$345$	6.40824	+	11.0994i	0.345008	+	0.597571i
$346$	−0.148165	+	0.138933i	−0.00796539	+	0.00746910i
$347$	2.40670	−	4.16854i	0.129199	−	0.223779i	−0.794168	−	0.607699i	$-0.792093\pi$
$347$	2.40670	−	4.16854i	0.129199	−	0.223779i	0.923366	+	0.383920i	$0.125426\pi$
$348$	−0.331443	+	5.14859i	−0.0177672	+	0.275993i
$349$	−35.4792			−1.89916			−0.949578	−	0.313530i	$-0.898488\pi$
$349$	−35.4792			−1.89916			−0.949578	+	0.313530i	$0.898488\pi$
$350$	1.15889	+	4.58929i	0.0619455	+	0.245308i
$351$		−	5.31228i		−	0.283549i
$352$	−26.0455	+	18.7788i	−1.38823	+	1.00091i
$353$	−4.13712	−	2.38857i	−0.220197	−	0.127131i	0.385845	−	0.922564i	$-0.373910\pi$
$353$	−4.13712	−	2.38857i	−0.220197	−	0.127131i	−0.606041	+	0.795433i	$0.707243\pi$
$354$	−10.4422	+	9.79162i	−0.554998	+	0.520419i
$355$	15.9375	−	9.20155i	0.845877	−	0.488367i
$356$	−7.57416	+	11.3641i	−0.401430	+	0.602297i
$357$	0.583186	−	1.05269i	0.0308655	−	0.0557145i
$358$	−25.6158	−	7.75419i	−1.35383	−	0.409822i
$359$	31.9690	−	18.4573i	1.68726	−	0.974140i	0.730656	−	0.682745i	$-0.239214\pi$
$359$	31.9690	−	18.4573i	1.68726	−	0.974140i	0.956603	−	0.291394i	$-0.0941192\pi$
$360$	−6.98299	+	1.16541i	−0.368036	+	0.0614227i
$361$	−2.67598	+	4.63493i	−0.140841	+	0.243943i
$362$	−7.15533	−	30.6070i	−0.376076	−	1.60867i
$363$		−	21.2191i		−	1.11371i
$364$	23.6629	+	15.1736i	1.24027	+	0.795310i
$365$			17.1547i			0.897916i
$366$	−6.89047	+	1.61086i	−0.360171	+	0.0842009i
$367$	0.284416	−	0.492623i	0.0148464	−	0.0257147i	−0.858507	−	0.512802i	$-0.828607\pi$
$367$	0.284416	−	0.492623i	0.0148464	−	0.0257147i	0.873353	+	0.487088i	$0.161941\pi$
$368$	2.62616	−	20.3127i	0.136898	−	1.05887i
$369$	−4.03301	+	2.32846i	−0.209950	+	0.121215i
$370$	−9.24623	+	30.5447i	−0.480689	+	1.58794i
$371$	−0.292503	−	16.5290i	−0.0151860	−	0.858143i
$372$	−6.66262	+	9.99647i	−0.345441	+	0.518293i
$373$	20.2929	−	11.7161i	1.05073	−	0.606638i	0.127874	−	0.991790i	$-0.459185\pi$
$373$	20.2929	−	11.7161i	1.05073	−	0.606638i	0.922853	+	0.385153i	$0.125851\pi$
$374$	2.49755	+	2.66350i	0.129145	+	0.137726i
$375$	8.09615	+	4.67431i	0.418083	+	0.241380i
$376$	0.949728	−	2.53678i	0.0489785	−	0.130824i
$377$			13.7037i			0.705775i
$378$	2.60725	+	2.68370i	0.134102	+	0.138035i
$379$	−14.7240			−0.756320			−0.378160	−	0.925740i	$-0.623443\pi$
$379$	−14.7240			−0.756320			−0.378160	+	0.925740i	$0.623443\pi$
$380$	18.4556	+	1.18809i	0.946755	+	0.0609479i
$381$	−3.19875	+	5.54040i	−0.163877	+	0.283843i
$382$	11.4059	+	12.1638i	0.583577	+	0.622353i
$383$	−2.49754	−	4.32587i	−0.127618	−	0.221042i	0.795135	−	0.606432i	$-0.207400\pi$
$383$	−2.49754	−	4.32587i	−0.127618	−	0.221042i	−0.922753	+	0.385391i	$0.874067\pi$
$384$	9.99943	+	5.29259i	0.510281	+	0.270086i
$385$	19.3678	+	32.2159i	0.987077	+	1.64187i
$386$	36.3057	+	10.9902i	1.84791	+	0.559385i
$387$	1.83351	+	3.17574i	0.0932028	+	0.161432i
$388$	−3.29191	−	6.65581i	−0.167122	−	0.337898i
$389$	−27.6098	−	15.9405i	−1.39987	−	0.808216i	−0.405492	−	0.914099i	$-0.632900\pi$
$389$	−27.6098	−	15.9405i	−1.39987	−	0.808216i	−0.994379	+	0.105883i	$0.966233\pi$
$390$	−18.3106	+	4.28067i	−0.927195	+	0.216760i
$391$	−2.32907			−0.117786
$392$	−19.4013	+	3.94816i	−0.979916	+	0.199412i
$393$	−14.5026			−0.731559
$394$	22.8378	−	5.33902i	1.15055	−	0.268976i
$395$	−19.3203	−	11.1546i	−0.972108	−	0.561247i
$396$	−10.1758	+	5.03286i	−0.511353	+	0.252911i
$397$	16.4530	+	28.4975i	0.825753	+	1.43025i	0.901343	+	0.433107i	$0.142583\pi$
$397$	16.4530	+	28.4975i	0.825753	+	1.43025i	−0.0755896	+	0.997139i	$0.524084\pi$
$398$	−15.4419	−	4.67445i	−0.774033	−	0.234309i
$399$	−5.03614	−	8.37697i	−0.252122	−	0.419373i
$400$	1.94731	+	4.67047i	0.0973655	+	0.233523i
$401$	−0.106236	−	0.184006i	−0.00530517	−	0.00918883i	0.863361	−	0.504587i	$-0.168355\pi$
$401$	−0.106236	−	0.184006i	−0.00530517	−	0.00918883i	−0.868666	+	0.495399i	$0.835022\pi$
$402$	−8.99889	−	9.59682i	−0.448824	−	0.478646i
$403$	−15.9545	+	27.6341i	−0.794752	+	1.37655i
$404$	−0.729994	+	11.3396i	−0.0363186	+	0.564167i
$405$	−2.50301			−0.124375
$406$	−6.72571	−	6.92294i	−0.333792	−	0.343580i
$407$			51.1745i			2.53663i
$408$	0.451080	−	1.20486i	0.0223318	−	0.0596496i
$409$	17.7288	+	10.2357i	0.876633	+	0.506124i	0.869547	−	0.493851i	$-0.164411\pi$
$409$	17.7288	+	10.2357i	0.876633	+	0.506124i	0.00708628	+	0.999975i	$0.497744\pi$
$410$	11.2757	+	12.0249i	0.556866	+	0.593867i
$411$	−1.06618	+	0.615559i	−0.0525908	+	0.0303633i
$412$	−9.83046	−	6.55198i	−0.484312	−	0.322793i
$413$	−0.473847	−	26.7765i	−0.0233165	−	1.31759i
$414$	2.09803	−	6.93080i	0.103113	−	0.340630i
$415$	−4.25425	+	2.45619i	−0.208833	+	0.120570i
$416$	27.4081	+	12.3225i	1.34379	+	0.604162i
$417$	−7.88942	+	13.6649i	−0.386347	+	0.669172i
$418$	28.8770	−	6.75088i	1.41242	−	0.330196i
$419$		−	11.8439i		−	0.578614i	−0.957236	−	0.289307i	$-0.906575\pi$
$419$		−	11.8439i		−	0.578614i	0.957236	−	0.289307i	$-0.0934248\pi$
$420$	7.14938	−	11.1493i	0.348854	−	0.544032i
$421$			21.7928i			1.06211i	0.847336	+	0.531057i	$0.178205\pi$
$421$			21.7928i			1.06211i	−0.847336	+	0.531057i	$0.821795\pi$
$422$	1.33056	+	5.69148i	0.0647705	+	0.277057i
$423$	0.478841	−	0.829377i	0.0232820	−	0.0403257i
$424$	−2.90927	−	17.4319i	−0.141287	−	0.846569i
$425$	0.498323	−	0.287707i	0.0241722	−	0.0139558i
$426$	−9.95188	−	3.01255i	−0.482170	−	0.145959i
$427$	6.41534	−	11.5802i	0.310460	−	0.560404i
$428$	−17.7422	−	11.8251i	−0.857601	−	0.571589i
$429$	−26.1137	+	15.0768i	−1.26078	+	0.727912i
$430$	9.46884	−	8.87888i	0.456628	−	0.428177i
$431$	−14.3234	−	8.26964i	−0.689936	−	0.398335i	0.113652	−	0.993521i	$-0.463745\pi$
$431$	−14.3234	−	8.26964i	−0.689936	−	0.398335i	−0.803588	+	0.595186i	$0.797078\pi$
$432$	3.17907	+	2.42766i	0.152953	+	0.116801i
$433$		−	39.2724i		−	1.88731i	−0.330929	−	0.943656i	$-0.607362\pi$
$433$		−	39.2724i		−	1.88731i	0.330929	−	0.943656i	$-0.392638\pi$
$434$	−5.50266	−	21.7908i	−0.264136	−	1.04599i
$435$	6.45681			0.309580
$436$	−6.34509	−	0.408469i	−0.303875	−	0.0195621i
$437$	−9.45828	+	16.3822i	−0.452451	+	0.783668i
$438$	7.07034	−	6.62982i	0.337834	−	0.316785i
$439$	−15.5165	−	26.8754i	−0.740564	−	1.28269i	−0.952239	−	0.305355i	$-0.901225\pi$
$439$	−15.5165	−	26.8754i	−0.740564	−	1.28269i	0.211674	−	0.977340i	$-0.432108\pi$
$440$	25.5472	+	31.0189i	1.21792	+	1.47877i
$441$	−6.99562	+	0.247671i	−0.333125	+	0.0117939i
$442$	0.990063	−	3.27064i	0.0470925	−	0.155569i
$443$	0.422464	+	0.731729i	0.0200719	+	0.0347655i	0.875887	−	0.482517i	$-0.160277\pi$
$443$	0.422464	+	0.731729i	0.0200719	+	0.0347655i	−0.855815	+	0.517282i	$0.826944\pi$
$444$	16.1625	−	7.99384i	0.767038	−	0.379371i
$445$	14.8018	+	8.54583i	0.701673	+	0.405111i
$446$	5.82906	+	24.9339i	0.276014	+	1.18066i
$447$	−5.95556			−0.281688
$448$	−19.8941	+	7.22661i	−0.939909	+	0.341425i
$449$	−41.7433			−1.96999			−0.984995	−	0.172585i	$-0.944788\pi$
$449$	−41.7433			−1.96999			−0.984995	+	0.172585i	$0.944788\pi$
$450$	0.407261	+	1.74207i	0.0191985	+	0.0821218i
$451$	22.8921	+	13.2168i	1.07795	+	0.622354i
$452$	0.542201	−	0.268168i	0.0255030	−	0.0126136i
$453$	1.79629	+	3.11126i	0.0843968	+	0.146180i
$454$	3.24726	−	10.7272i	0.152401	−	0.503453i
$455$	17.0480	−	30.7730i	0.799224	−	1.44266i
$456$	−6.64294	−	8.06571i	−0.311084	−	0.377712i
$457$	3.74286	+	6.48282i	0.175083	+	0.303254i	0.940190	−	0.340650i	$-0.110647\pi$
$457$	3.74286	+	6.48282i	0.175083	+	0.303254i	−0.765107	+	0.643904i	$0.777314\pi$
$458$	2.22390	−	2.08534i	0.103916	−	0.0974415i
$459$	0.227429	−	0.393919i	0.0106155	−	0.0183865i
$460$	−25.5800	−	1.64673i	−1.19267	−	0.0767791i
$461$	4.33499			0.201901			0.100950	−	0.994891i	$-0.467812\pi$
$461$	4.33499			0.201901			0.100950	+	0.994891i	$0.467812\pi$
$462$	5.79272	−	20.4331i	0.269502	−	0.950634i
$463$			35.3200i			1.64146i	0.571316	+	0.820730i	$0.306433\pi$
$463$			35.3200i			1.64146i	−0.571316	+	0.820730i	$0.693567\pi$
$464$	−8.20080	−	6.26244i	−0.380712	−	0.290726i
$465$	13.0204	+	7.51736i	0.603809	+	0.348609i
$466$	20.6473	−	19.3609i	0.956467	−	0.896874i
$467$	9.09213	−	5.24934i	0.420733	−	0.242911i	−0.274658	−	0.961542i	$-0.588565\pi$
$467$	9.09213	−	5.24934i	0.420733	−	0.242911i	0.695391	+	0.718632i	$0.255231\pi$
$468$	8.84086	+	5.89241i	0.408669	+	0.272377i
$469$	24.6087	−	0.435484i	1.13632	−	0.0201088i
$470$	−3.24459	−	0.982175i	−0.149662	−	0.0453044i
$471$	−0.851757	+	0.491762i	−0.0392469	+	0.0226592i
$472$	−4.71293	−	28.2392i	−0.216930	−	1.29981i
$473$	10.4074	−	18.0261i	0.478532	−	0.828841i
$474$	2.86939	+	12.2738i	0.131795	+	0.563756i
$475$		−	4.67348i		−	0.214434i
$476$	1.10505	+	2.13821i	0.0506500	+	0.0980047i
$477$		−	6.24836i		−	0.286093i
$478$	−26.0163	+	6.08210i	−1.18996	+	0.278189i
$479$	8.46375	−	14.6596i	0.386719	−	0.669816i	−0.605287	−	0.796007i	$-0.706942\pi$
$479$	8.46375	−	14.6596i	0.386719	−	0.669816i	0.992006	+	0.126191i	$0.0402752\pi$
$480$	5.80606	−	12.9140i	0.265009	−	0.589440i
$481$	41.4771	−	23.9468i	1.89119	−	1.09188i
$482$	−7.50161	+	24.7814i	−0.341689	+	1.12876i
$483$	6.98022	+	11.6107i	0.317611	+	0.528305i
$484$	35.3135	+	23.5364i	1.60516	+	1.06983i
$485$	−8.04790	+	4.64645i	−0.365436	+	0.210985i
$486$	0.967346	+	1.03162i	0.0438797	+	0.0467953i
$487$	20.5482	+	11.8635i	0.931127	+	0.537586i	0.887168	−	0.461447i	$-0.152670\pi$
$487$	20.5482	+	11.8635i	0.931127	+	0.537586i	0.0439591	+	0.999033i	$0.486003\pi$
$488$	4.96211	−	13.2541i	0.224624	−	0.599985i
$489$		−	2.52167i		−	0.114034i
$490$	6.49079	+	23.9133i	0.293224	+	1.08029i
$491$	−3.41198			−0.153980			−0.0769901	−	0.997032i	$-0.524531\pi$
$491$	−3.41198			−0.153980			−0.0769901	+	0.997032i	$0.524531\pi$
$492$	0.598345	−	9.29460i	0.0269755	−	0.419033i
$493$	−0.586681	+	1.01616i	−0.0264228	+	0.0457656i
$494$	−18.9844	−	20.2459i	−0.854151	−	0.910905i
$495$	7.10377	+	12.3041i	0.319291	+	0.553028i
$496$	−9.24621	−	22.1763i	−0.415167	−	0.995744i
$497$	16.6717	−	10.0229i	0.747829	−	0.449587i
$498$	2.65648	+	0.804149i	0.119040	+	0.0360348i
$499$	8.72998	+	15.1208i	0.390808	+	0.676899i	0.992556	−	0.121787i	$-0.0388624\pi$
$499$	8.72998	+	15.1208i	0.390808	+	0.676899i	−0.601749	+	0.798686i	$0.705529\pi$
$500$	−16.7594	+	8.28908i	−0.749504	+	0.370699i
$501$	−4.55730	−	2.63116i	−0.203605	−	0.117552i
$502$	4.72685	−	1.10505i	0.210970	−	0.0493206i
$503$	7.08646			0.315970			0.157985	−	0.987442i	$-0.449500\pi$
$503$	7.08646			0.315970			0.157985	+	0.987442i	$0.449500\pi$
$504$	−7.35827	+	1.36228i	−0.327764	+	0.0606809i
$505$	14.2209			0.632824
$506$	−40.0243	+	9.35690i	−1.77930	+	0.415965i
$507$	13.1812	+	7.61017i	0.585397	+	0.337979i
$508$	−5.67243	−	11.4689i	−0.251673	−	0.508851i
$509$	18.9653	+	32.8488i	0.840622	+	1.45600i	0.889370	+	0.457188i	$0.151143\pi$
$509$	18.9653	+	32.8488i	0.840622	+	1.45600i	−0.0487485	+	0.998811i	$0.515523\pi$
$510$	−1.54104	−	0.466491i	−0.0682385	−	0.0206566i
$511$	0.320837	+	18.1301i	0.0141930	+	0.802030i
$512$	−19.8995	+	10.7708i	−0.879442	+	0.476006i
$513$	−1.84716	−	3.19938i	−0.0815543	−	0.141256i
$514$	−24.2504	−	25.8618i	−1.06964	−	1.14071i
$515$	−7.39252	+	12.8042i	−0.325753	+	0.564221i
$516$	−7.31891	−	0.471159i	−0.322197	−	0.0207416i
$517$	−5.43598			−0.239074
$518$	−9.20074	+	32.4545i	−0.404257	+	1.42597i
$519$		−	0.143623i		−	0.00630436i
$520$	13.1862	−	35.2212i	0.578255	−	1.54455i
$521$	6.91166	+	3.99045i	0.302805	+	0.174825i	0.643702	−	0.765276i	$-0.277397\pi$
$521$	6.91166	+	3.99045i	0.302805	+	0.174825i	−0.340897	+	0.940101i	$0.610731\pi$
$522$	−2.49539	−	2.66119i	−0.109220	−	0.116477i
$523$	12.3267	−	7.11681i	0.539008	−	0.311196i	−0.205669	−	0.978622i	$-0.565937\pi$
$523$	12.3267	−	7.11681i	0.539008	−	0.311196i	0.744677	+	0.667425i	$0.232604\pi$
$524$	16.0864	−	24.1357i	0.702736	−	1.05437i
$525$	−2.92773	−	1.62194i	−0.127777	−	0.0707874i
$526$	6.35470	−	20.9926i	0.277078	−	0.915320i
$527$	−2.36614	+	1.36609i	−0.103071	+	0.0595078i
$528$	2.91120	−	22.5173i	0.126694	−	0.979941i
$529$	1.60942	−	2.78759i	0.0699747	−	0.121200i
$530$	−21.5371	+	5.03496i	−0.935513	+	0.218705i
$531$		−	10.1222i		−	0.439264i
$532$	19.5273	+	0.910483i	0.846617	+	0.0394744i
$533$		−	24.7389i		−	1.07156i
$534$	−2.19832	−	9.40335i	−0.0951306	−	0.406923i
$535$	−13.3421	+	23.1093i	−0.576831	+	0.999101i
$536$	25.9529	−	4.33137i	1.12100	−	0.187087i
$537$	16.3893	−	9.46239i	0.707252	−	0.408332i
$538$	32.1244	+	9.72444i	1.38498	+	0.419250i
$539$	21.0717	+	33.6856i	0.907622	+	1.45094i
$540$	2.77635	−	4.16558i	0.119475	−	0.179258i
$541$	−6.43282	+	3.71399i	−0.276569	+	0.159677i	−0.631869	−	0.775075i	$-0.717712\pi$
$541$	−6.43282	+	3.71399i	−0.276569	+	0.159677i	0.355300	+	0.934752i	$0.384379\pi$
$542$	15.1790	−	14.2332i	0.651992	−	0.611369i
$543$	19.2483	+	11.1130i	0.826022	+	0.476904i
$544$	1.50483	+	2.08714i	0.0645190	+	0.0894855i
$545$			7.95734i			0.340855i
$546$	−19.2718	+	4.86654i	−0.824756	+	0.208269i
$547$	−28.2287			−1.20697			−0.603485	−	0.797374i	$-0.706222\pi$
$547$	−28.2287			−1.20697			−0.603485	+	0.797374i	$0.706222\pi$
$548$	0.158181	−	2.45715i	0.00675714	−	0.104964i
$549$	2.50184	−	4.33331i	0.106776	−	0.184941i
$550$	7.40767	−	6.94613i	0.315864	−	0.296184i
$551$	4.76498	+	8.25319i	0.202995	+	0.351598i
$552$	9.20729	+	11.1793i	0.391888	+	0.475822i
$553$	−20.6275	−	11.4275i	−0.877171	−	0.485947i
$554$	2.91834	−	9.64064i	0.123988	−	0.409592i
$555$	−11.2831	−	19.5429i	−0.478941	−	0.829551i
$556$	−13.9905	−	28.2870i	−0.593330	−	1.19963i
$557$	29.9378	+	17.2846i	1.26850	+	0.732371i	0.974705	−	0.223496i	$-0.0717470\pi$
$557$	29.9378	+	17.2846i	1.26850	+	0.732371i	0.293799	+	0.955867i	$0.405080\pi$
$558$	−1.93376	−	8.27167i	−0.0818624	−	0.350168i
$559$	−19.4803			−0.823929
$560$	10.6249	+	24.2651i	0.448985	+	1.02539i
$561$	−2.58186			−0.109006
$562$	4.20321	+	17.9793i	0.177302	+	0.758412i
$563$	−10.1504	−	5.86033i	−0.427788	−	0.246983i	0.270616	−	0.962687i	$-0.412773\pi$
$563$	−10.1504	−	5.86033i	−0.427788	−	0.246983i	−0.698404	+	0.715704i	$0.746106\pi$
$564$	0.849141	+	1.71685i	0.0357553	+	0.0722925i
$565$	−0.378513	−	0.655603i	−0.0159242	−	0.0275814i
$566$	−0.866059	+	2.86100i	−0.0364032	+	0.120257i
$567$	−2.64534	+	0.0468128i	−0.111094	+	0.00196595i
$568$	16.0523	−	13.2207i	0.673538	−	0.554728i
$569$	5.55324	+	9.61849i	0.232804	+	0.403228i	0.958632	−	0.284648i	$-0.0918766\pi$
$569$	5.55324	+	9.61849i	0.232804	+	0.403228i	−0.725828	+	0.687876i	$0.758543\pi$
$570$	−9.53932	+	8.94497i	−0.399558	+	0.374664i
$571$	17.7557	−	30.7537i	0.743052	−	1.28700i	−0.208047	−	0.978119i	$-0.566711\pi$
$571$	17.7557	−	30.7537i	0.743052	−	1.28700i	0.951099	−	0.308885i	$-0.0999558\pi$
$572$	3.87428	−	60.1824i	0.161992	−	2.51635i
$573$	−11.7909			−0.492573
$574$	12.1417	+	12.4978i	0.506787	+	0.521648i
$575$			6.47756i			0.270133i
$576$	−7.56642	+	2.59793i	−0.315268	+	0.108247i
$577$	−23.4304	−	13.5276i	−0.975421	−	0.563159i	−0.0745363	−	0.997218i	$-0.523748\pi$
$577$	−23.4304	−	13.5276i	−0.975421	−	0.563159i	−0.900885	+	0.434059i	$0.857081\pi$
$578$	−17.3241	+	16.2447i	−0.720589	+	0.675692i
$579$	−23.2289	+	13.4112i	−0.965361	+	0.557351i
$580$	−7.16193	+	10.7456i	−0.297383	+	0.446188i
$581$	−4.45023	+	2.67543i	−0.184627	+	0.110995i
$582$	5.02535	+	1.52123i	0.208307	+	0.0630571i
$583$	−30.7152	+	17.7334i	−1.27209	+	0.734443i
$584$	3.19108	+	19.1205i	0.132048	+	0.791212i
$585$	6.64834	−	11.5153i	0.274875	−	0.476097i
$586$	−0.107527	−	0.459948i	−0.00444190	−	0.0190003i
$587$		−	35.3797i		−	1.46027i	−0.683300	−	0.730137i	$-0.739456\pi$
$587$		−	35.3797i		−	1.46027i	0.683300	−	0.730137i	$-0.260544\pi$
$588$	7.34740	−	11.9170i	0.303002	−	0.491450i
$589$			22.1906i			0.914347i
$590$	−34.8895	+	8.15649i	−1.43638	+	0.335797i
$591$	−8.29208	+	14.3623i	−0.341091	+	0.590786i
$592$	−4.62394	+	35.7649i	−0.190043	+	1.46993i
$593$	−33.9659	+	19.6102i	−1.39481	+	0.805294i	−0.993843	−	0.110798i	$-0.964659\pi$
$593$	−33.9659	+	19.6102i	−1.39481	+	0.805294i	−0.400968	+	0.916092i	$0.631326\pi$
$594$	2.32575	−	7.68304i	0.0954266	−	0.315239i
$595$	2.58160	−	1.55203i	0.105835	−	0.0636271i
$596$	6.60594	−	9.91142i	0.270590	−	0.405988i
$597$	9.87996	−	5.70420i	0.404360	−	0.233457i
$598$	26.3129	+	28.0613i	1.07602	+	1.14751i
$599$	−41.2853	−	23.8361i	−1.68687	−	0.973916i	−0.956890	−	0.290450i	$-0.906195\pi$
$599$	−41.2853	−	23.8361i	−1.68687	−	0.973916i	−0.729982	−	0.683466i	$-0.760472\pi$
$600$	−3.35094	−	1.25453i	−0.136801	−	0.0512161i
$601$		−	13.4207i		−	0.547442i	−0.961809	−	0.273721i	$-0.911746\pi$
$601$		−	13.4207i		−	0.547442i	0.961809	−	0.273721i	$-0.0882544\pi$
$602$	9.84121	−	9.56086i	0.401098	−	0.389671i
$603$	9.30266			0.378834
$604$	−7.17030	−	0.461592i	−0.291755	−	0.0187819i
$605$	26.5558	−	45.9960i	1.07965	−	1.87000i
$606$	−5.49602	−	5.86120i	−0.223260	−	0.238095i
$607$	−19.1391	−	33.1498i	−0.776831	−	1.34551i	−0.933760	−	0.357901i	$-0.883493\pi$
$607$	−19.1391	−	33.1498i	−0.776831	−	1.34551i	0.156929	−	0.987610i	$-0.449841\pi$
$608$	20.7916	−	2.10885i	0.843210	−	0.0855251i
$609$	6.82397	−	0.120759i	0.276521	−	0.00489342i
$610$	−16.9522	−	5.13164i	−0.686376	−	0.207774i
$611$	2.54374	+	4.40588i	0.102909	+	0.178243i
$612$	0.403306	+	0.815431i	0.0163027	+	0.0329619i
$613$	16.9225	+	9.77021i	0.683493	+	0.394615i	0.801170	−	0.598437i	$-0.204211\pi$
$613$	16.9225	+	9.77021i	0.683493	+	0.394615i	−0.117677	+	0.993052i	$0.537545\pi$
$614$	−12.9328	+	3.02343i	−0.521923	+	0.122016i
$615$	−11.6563			−0.470028
$616$	27.5801	+	32.3049i	1.11123	+	1.30160i
$617$	−1.16195			−0.0467785			−0.0233892	−	0.999726i	$-0.507446\pi$
$617$	−1.16195			−0.0467785			−0.0233892	+	0.999726i	$0.507446\pi$
$618$	8.13430	−	1.90164i	0.327210	−	0.0764953i
$619$	31.0842	+	17.9465i	1.24938	+	0.721330i	0.970986	−	0.239137i	$-0.0768645\pi$
$619$	31.0842	+	17.9465i	1.24938	+	0.721330i	0.278394	+	0.960467i	$0.410198\pi$
$620$	−26.9530	+	13.3307i	−1.08246	+	0.535375i
$621$	2.56022	+	4.43443i	0.102738	+	0.177947i
$622$	−21.4877	−	6.50459i	−0.861579	−	0.260810i
$623$	15.8033	+	8.75495i	0.633147	+	0.350759i
$624$	−19.6127	+	8.17733i	−0.785135	+	0.327355i
$625$	14.8624	+	25.7425i	0.594498	+	1.02970i
$626$	31.1153	+	33.1827i	1.24362	+	1.32625i
$627$	−10.4848	+	18.1603i	−0.418724	+	0.725252i
$628$	0.126368	−	1.96298i	0.00504264	−	0.0783316i
$629$	4.10084			0.163511
$630$	2.29298	+	9.08035i	0.0913547	+	0.361770i
$631$			8.26460i			0.329008i	0.986376	+	0.164504i	$0.0526024\pi$
$631$			8.26460i			0.329008i	−0.986376	+	0.164504i	$0.947398\pi$
$632$	−23.6092	−	8.83890i	−0.939125	−	0.351593i
$633$	−3.57928	−	2.06650i	−0.142264	−	0.0821360i
$634$	−14.7725	−	15.7540i	−0.586690	−	0.625673i
$635$	−13.8677	+	8.00650i	−0.550322	+	0.317728i
$636$	10.3987	+	6.93071i	0.412335	+	0.274821i
$637$	17.4419	−	32.8417i	0.691074	−	1.30123i
$638$	−5.99955	+	19.8193i	−0.237524	+	0.784655i
$639$	6.36736	−	3.67620i	0.251889	−	0.145428i
$640$	15.0517	+	23.9869i	0.594972	+	0.948165i
$641$	−14.4955	+	25.1070i	−0.572539	+	0.991666i	0.423766	+	0.905772i	$0.360708\pi$
$641$	−14.4955	+	25.1070i	−0.572539	+	0.991666i	−0.996304	+	0.0858940i	$0.972625\pi$
$642$	14.6809	−	3.43212i	0.579410	−	0.135455i
$643$			39.1239i			1.54289i	0.636293	+	0.771447i	$0.280467\pi$
$643$			39.1239i			1.54289i	−0.636293	+	0.771447i	$0.719533\pi$
$644$	−27.0654	−	1.26195i	−1.06653	−	0.0497279i
$645$			9.17860i			0.361407i
$646$	−0.540978	−	2.31404i	−0.0212845	−	0.0910448i
$647$	6.09491	−	10.5567i	0.239616	−	0.415027i	−0.720988	−	0.692947i	$-0.756312\pi$
$647$	6.09491	−	10.5567i	0.239616	−	0.415027i	0.960604	+	0.277921i	$0.0896452\pi$
$648$	−2.78984	+	0.465606i	−0.109595	+	0.0182907i
$649$	−49.7577	+	28.7276i	−1.95316	+	1.12766i
$650$	−9.09624	−	2.75354i	−0.356784	−	0.108003i
$651$	13.9014	+	7.70131i	0.544840	+	0.301838i
$652$	4.19664	+	2.79705i	0.164353	+	0.109541i
$653$	8.80194	−	5.08180i	0.344446	−	0.198866i	−0.317790	−	0.948161i	$-0.602941\pi$
$653$	8.80194	−	5.08180i	0.344446	−	0.198866i	0.662237	+	0.749295i	$0.269607\pi$
$654$	3.27964	−	3.07530i	0.128244	−	0.120254i
$655$	−31.4368	−	18.1500i	−1.22834	−	0.709181i
$656$	14.8047	+	11.3054i	0.578025	+	0.441402i
$657$			6.85362i			0.267385i
$658$	−3.44746	−	0.977343i	−0.134396	−	0.0381008i
$659$	−8.28558			−0.322760			−0.161380	−	0.986892i	$-0.551595\pi$
$659$	−8.28558			−0.322760			−0.161380	+	0.986892i	$0.551595\pi$
$660$	−28.3564	−	1.82546i	−1.10377	−	0.0710558i
$661$	8.30890	−	14.3914i	0.323179	−	0.559762i	−0.657963	−	0.753050i	$-0.728582\pi$
$661$	8.30890	−	14.3914i	0.323179	−	0.559762i	0.981142	+	0.193288i	$0.0619151\pi$
$662$	21.7031	−	20.3509i	0.843516	−	0.790961i
$663$	1.20817	+	2.09261i	0.0469213	+	0.0812701i
$664$	−4.28487	+	3.52903i	−0.166285	+	0.136953i
$665$	−0.432875	−	24.4612i	−0.0167862	−	0.948566i
$666$	−3.69405	+	12.2032i	−0.143141	+	0.472864i
$667$	−6.60439	−	11.4391i	−0.255723	−	0.442925i
$668$	9.43384	−	4.66590i	0.365006	−	0.180529i
$669$	−15.6805	−	9.05316i	−0.606245	−	0.350016i
$670$	−7.49614	−	32.0649i	−0.289601	−	1.23877i
$671$	−28.4018			−1.09644
$672$	5.89468	−	13.7569i	0.227392	−	0.530684i
$673$	13.1599			0.507278			0.253639	−	0.967299i	$-0.418372\pi$
$673$	13.1599			0.507278			0.253639	+	0.967299i	$0.418372\pi$
$674$	−0.381012	−	1.62979i	−0.0146760	−	0.0627770i
$675$	−1.09556	−	0.632521i	−0.0421680	−	0.0243457i
$676$	−27.2857	+	13.4953i	−1.04945	+	0.519050i
$677$	−10.2201	−	17.7017i	−0.392790	−	0.680332i	0.600026	−	0.799980i	$-0.295157\pi$
$677$	−10.2201	−	17.7017i	−0.392790	−	0.680332i	−0.992816	+	0.119648i	$0.961823\pi$
$678$	−0.123924	+	0.409378i	−0.00475926	+	0.0157221i
$679$	−8.41863	+	5.06119i	−0.323077	+	0.194231i
$680$	2.48568	−	2.04721i	0.0953215	−	0.0785070i
$681$	3.96260	+	6.86343i	0.151847	+	0.263007i
$682$	−35.1731	+	32.9816i	−1.34685	+	1.26293i
$683$	7.87273	−	13.6360i	0.301242	−	0.521766i	−0.675176	−	0.737657i	$-0.735932\pi$
$683$	7.87273	−	13.6360i	0.301242	−	0.521766i	0.976418	+	0.215891i	$0.0692655\pi$
$684$	7.37339	+	0.474666i	0.281929	+	0.0181493i
$685$	−3.08150			−0.117738
$686$	7.30713	+	25.1517i	0.278987	+	0.960295i
$687$			2.15573i			0.0822464i
$688$	8.90229	−	11.6577i	0.339397	−	0.444447i
$689$	28.7460	+	16.5965i	1.09514	+	0.632277i
$690$	13.2218	−	12.3980i	0.503343	−	0.471982i
$691$	2.76346	−	1.59549i	0.105127	−	0.0606952i	−0.446515	−	0.894776i	$-0.647335\pi$
$691$	2.76346	−	1.59549i	0.105127	−	0.0606952i	0.551642	+	0.834081i	$0.314002\pi$
$692$	0.239022	+	0.159308i	0.00908626	+	0.00605597i
$693$	7.73783	+	12.8709i	0.293936	+	0.488924i
$694$	−6.51522	−	1.97223i	−0.247314	−	0.0748650i
$695$	−34.2033	+	19.7473i	−1.29740	+	0.749057i
$696$	7.19673	−	1.20109i	0.272792	−	0.0455271i
$697$	1.05912	−	1.83445i	0.0401170	−	0.0694847i
$698$	11.4220	+	48.8578i	0.432329	+	1.84929i
$699$			20.0144i			0.757015i
$700$	5.94674	−	3.07335i	0.224766	−	0.116162i
$701$		−	39.2121i		−	1.48102i	−0.672045	−	0.740511i	$-0.734584\pi$
$701$		−	39.2121i		−	1.48102i	0.672045	−	0.740511i	$-0.265416\pi$
$702$	−7.31545	+	1.71021i	−0.276104	+	0.0645477i
$703$	16.6534	−	28.8445i	0.628094	−	1.08789i
$704$	34.2449	+	29.8213i	1.29065	+	1.12393i
$705$	2.07594	−	1.19854i	0.0781843	−	0.0451397i
$706$	−1.95737	+	6.46612i	−0.0736666	+	0.243356i
$707$	15.0296	−	0.265969i	0.565246	−	0.0100028i
$708$	16.8456	+	11.2275i	0.633096	+	0.421957i
$709$	33.3653	−	19.2635i	1.25306	−	0.723454i	0.281343	−	0.959607i	$-0.409220\pi$
$709$	33.3653	−	19.2635i	1.25306	−	0.723454i	0.971716	+	0.236153i	$0.0758867\pi$
$710$	−17.8022	−	18.9850i	−0.668103	−	0.712495i
$711$	−7.71882	−	4.45646i	−0.289478	−	0.167130i
$712$	18.0877	+	6.77174i	0.677866	+	0.253782i
$713$		−	30.7567i		−	1.15185i
$714$	−1.63740	−	0.464196i	−0.0612780	−	0.0173721i
$715$	−75.4744			−2.82258
$716$	−2.43155	+	37.7714i	−0.0908714	+	1.41158i
$717$	9.44616	−	16.3612i	0.352773	−	0.611021i
$718$	−35.7092	−	38.0819i	−1.33266	−	1.42120i
$719$	11.5009	+	19.9202i	0.428912	+	0.742897i	0.996777	−	0.0802246i	$-0.0255637\pi$
$719$	11.5009	+	19.9202i	0.428912	+	0.742897i	−0.567865	+	0.823122i	$0.692230\pi$
$720$	3.85294	+	9.24097i	0.143591	+	0.344391i
$721$	−7.57341	+	13.6706i	−0.282049	+	0.509119i
$722$	7.24417	+	2.19289i	0.269600	+	0.0816111i
$723$	−9.15417	−	15.8555i	−0.340447	−	0.589672i
$724$	−39.8449	+	19.7070i	−1.48082	+	0.732403i
$725$	2.82613	+	1.63166i	0.104960	+	0.0605985i
$726$	−29.2205	+	6.83118i	−1.08447	+	0.253529i
$727$	21.8433			0.810125			0.405062	−	0.914289i	$-0.367250\pi$
$727$	21.8433			0.810125			0.405062	+	0.914289i	$0.367250\pi$
$728$	13.2773	−	37.4707i	0.492090	−	1.38876i
$729$	−1.00000			−0.0370370
$730$	23.6234	−	5.52269i	0.874341	−	0.204404i
$731$	−1.44451	−	0.833989i	−0.0534272	−	0.0308462i
$732$	4.43657	+	8.97016i	0.163980	+	0.331547i
$733$	−24.0681	−	41.6871i	−0.888974	−	1.53975i	−0.841089	−	0.540896i	$-0.818085\pi$
$733$	−24.0681	−	41.6871i	−0.888974	−	1.53975i	−0.0478850	−	0.998853i	$-0.515248\pi$
$734$	−0.769946	−	0.233072i	−0.0284192	−	0.00860283i
$735$	−15.4741	−	8.21817i	−0.570772	−	0.303132i
$736$	−28.8177	+	2.92292i	−1.06223	+	0.107740i
$737$	−26.4018	−	45.7293i	−0.972524	−	1.68446i
$738$	4.50485	+	4.80418i	0.165826	+	0.176844i
$739$	3.23455	−	5.60241i	0.118985	−	0.206088i	−0.800381	−	0.599492i	$-0.795369\pi$
$739$	3.23455	−	5.60241i	0.118985	−	0.206088i	0.919366	+	0.393404i	$0.128703\pi$
$740$	45.0392	+	2.89943i	1.65567	+	0.106585i
$741$	19.6253			0.720953
$742$	−22.6677	+	5.72407i	−0.832156	+	0.210137i
$743$		−	16.6709i		−	0.611597i	−0.952096	−	0.305798i	$-0.901077\pi$
$743$		−	16.6709i		−	0.611597i	0.952096	−	0.305798i	$-0.0989234\pi$
$744$	15.9109	+	5.95677i	0.583322	+	0.218386i
$745$	−12.9097	−	7.45340i	−0.472974	−	0.273072i
$746$	−22.6671	−	24.1732i	−0.829900	−	0.885043i
$747$	−1.69966	+	0.981297i	−0.0621872	+	0.0359038i
$748$	2.86381	−	4.29681i	0.104711	−	0.157107i
$749$	−13.6686	+	24.6729i	−0.499441	+	0.901528i
$750$	3.83048	−	12.6539i	0.139869	−	0.462055i
$751$	21.2698	−	12.2801i	0.776145	−	0.448108i	−0.0589171	−	0.998263i	$-0.518765\pi$
$751$	21.2698	−	12.2801i	0.776145	−	0.448108i	0.835062	+	0.550155i	$0.185431\pi$
$752$	−3.79911	−	0.491175i	−0.138539	−	0.0179113i
$753$	−1.71626	+	2.97264i	−0.0625439	+	0.108329i
$754$	18.8711	−	4.41170i	0.687245	−	0.160664i
$755$			8.99223i			0.327261i
$756$	2.85632	−	4.45438i	0.103883	−	0.162004i
$757$			2.80888i			0.102091i	0.998696	+	0.0510453i	$0.0162553\pi$
$757$			2.80888i			0.102091i	−0.998696	+	0.0510453i	$0.983745\pi$
$758$	4.74016	+	20.2761i	0.172171	+	0.736462i
$759$	14.5323	−	25.1706i	0.527488	−	0.913636i
$760$	−4.30542	−	25.7974i	−0.156174	−	0.935772i
$761$	−17.4708	+	10.0868i	−0.633317	+	0.365646i	−0.782036	−	0.623234i	$-0.785819\pi$
$761$	−17.4708	+	10.0868i	−0.633317	+	0.365646i	0.148718	+	0.988880i	$0.452485\pi$
$762$	8.65939	+	2.62130i	0.313697	+	0.0949596i
$763$	0.148823	+	8.40982i	0.00538776	+	0.304456i
$764$	13.0786	−	19.6228i	0.473166	−	0.709929i
$765$	0.985981	−	0.569256i	0.0356482	−	0.0205815i
$766$	−5.15303	+	4.83197i	−0.186187	+	0.174586i
$767$	46.5677	+	26.8859i	1.68146	+	0.970792i
$768$	4.06917	−	15.4739i	0.146833	−	0.558367i
$769$		−	32.1388i		−	1.15895i	−0.814988	−	0.579477i	$-0.803257\pi$
$769$		−	32.1388i		−	1.15895i	0.814988	−	0.579477i	$-0.196743\pi$
$770$	38.1288	−	37.0426i	1.37407	−	1.33492i
$771$	25.0690			0.902840
$772$	3.44629	−	53.5341i	0.124035	−	1.92673i
$773$	−11.2931	+	19.5603i	−0.406186	+	0.703534i	−0.994459	−	0.105128i	$-0.966475\pi$
$773$	−11.2931	+	19.5603i	−0.406186	+	0.703534i	0.588273	+	0.808662i	$0.299808\pi$
$774$	3.78299	−	3.54728i	0.135977	−	0.127505i
$775$	3.79934	+	6.58065i	0.136476	+	0.236384i
$776$	−8.10583	+	6.67598i	−0.290982	+	0.239654i
$777$	−12.2902	−	20.4432i	−0.440909	−	0.733395i
$778$	−13.0628	+	43.1528i	−0.468326	+	1.54710i
$779$	−8.60209	−	14.8993i	−0.308202	−	0.533822i
$780$	11.7897	+	23.8372i	0.422138	+	0.853507i
$781$	−36.1423	−	20.8668i	−1.29327	−	0.746673i
$782$	0.749810	+	3.20732i	0.0268131	+	0.114694i
$783$	2.57962			0.0921882
$784$	11.6829	+	25.4462i	0.417247	+	0.908793i
$785$	−2.46177			−0.0878642
$786$	4.66890	+	19.9713i	0.166534	+	0.712352i
$787$	−29.2593	−	16.8929i	−1.04298	−	0.602166i	−0.122306	−	0.992492i	$-0.539029\pi$
$787$	−29.2593	−	16.8929i	−1.04298	−	0.602166i	−0.920677	+	0.390326i	$0.872362\pi$
$788$	−14.7046	−	29.7307i	−0.523828	−	1.05911i
$789$	7.75460	+	13.4314i	0.276071	+	0.478169i
$790$	−9.14088	+	30.1967i	−0.325218	+	1.07435i
$791$	−0.412298	−	0.685804i	−0.0146596	−	0.0243844i
$792$	10.2066	+	12.3927i	0.362676	+	0.440354i
$793$	13.2905	+	23.0197i	0.471958	+	0.817455i
$794$	33.9466	−	31.8315i	1.20472	−	1.12966i
$795$	7.81984	−	13.5444i	0.277341	−	0.480369i
$796$	−1.46581	+	22.7697i	−0.0519543	+	0.807049i
$797$	27.0472			0.958061			0.479030	−	0.877798i	$-0.340988\pi$
$797$	27.0472			0.958061			0.479030	+	0.877798i	$0.340988\pi$
$798$	−9.91447	+	9.63203i	−0.350969	+	0.340970i
$799$			0.435609i			0.0154108i
$800$	5.80471	−	4.18519i	0.205228	−	0.147969i
$801$	5.91361	+	3.41423i	0.208947	+	0.120636i
$802$	−0.219191	+	0.205534i	−0.00773989	+	0.00725765i
$803$	33.6905	−	19.4512i	1.18891	−	0.686418i
$804$	−10.3186	+	15.4818i	−0.363908	+	0.546000i
$805$	0.599976	+	33.9039i	0.0211464	+	1.19496i
$806$	43.1907	+	13.0743i	1.52133	+	0.460524i
$807$	−20.5537	+	11.8667i	−0.723523	+	0.417726i
$808$	15.8506	−	2.64536i	0.557622	−	0.0930634i
$809$	24.9224	−	43.1669i	0.876226	−	1.51767i	0.0207751	−	0.999784i	$-0.493387\pi$
$809$	24.9224	−	43.1669i	0.876226	−	1.51767i	0.855451	−	0.517884i	$-0.173280\pi$
$810$	0.805806	+	3.44685i	0.0283131	+	0.121110i
$811$			36.5330i			1.28285i	0.767188	+	0.641423i	$0.221655\pi$
$811$			36.5330i			1.28285i	−0.767188	+	0.641423i	$0.778345\pi$
$812$	−7.36822	+	11.4906i	−0.258574	+	0.403241i
$813$			14.7137i			0.516031i
$814$	70.4715	−	16.4749i	2.47003	−	0.577444i
$815$	3.15588	−	5.46614i	0.110546	−	0.191470i
$816$	−1.80441	−	0.233287i	−0.0631671	−	0.00816669i
$817$	−11.7322	+	6.77360i	−0.410459	+	0.236978i
$818$	8.38793	−	27.7093i	0.293277	−	0.968832i
$819$	6.81102	−	12.2944i	0.237996	−	0.429601i
$820$	12.9292	−	19.3988i	0.451509	−	0.677435i
$821$	−2.59911	+	1.50060i	−0.0907095	+	0.0523711i	−0.544669	−	0.838651i	$-0.683345\pi$
$821$	−2.59911	+	1.50060i	−0.0907095	+	0.0523711i	0.453959	+	0.891023i	$0.350011\pi$
$822$	1.19092	+	1.27005i	0.0415380	+	0.0442980i
$823$	13.8543	+	7.99877i	0.482930	+	0.278820i	0.721637	−	0.692272i	$-0.243390\pi$
$823$	13.8543	+	7.99877i	0.482930	+	0.278820i	−0.238707	+	0.971092i	$0.576723\pi$
$824$	−5.85785	+	15.6467i	−0.204068	+	0.545078i
$825$			7.18061i			0.249997i
$826$	−36.7209	+	9.27282i	−1.27768	+	0.322643i
$827$	4.57856			0.159212			0.0796060	−	0.996826i	$-0.474634\pi$
$827$	4.57856			0.159212			0.0796060	+	0.996826i	$0.474634\pi$
$828$	−10.2197	−	0.657900i	−0.355160	−	0.0228636i
$829$	−1.53077	+	2.65136i	−0.0531657	+	0.0920857i	−0.891383	−	0.453250i	$-0.850264\pi$
$829$	−1.53077	+	2.65136i	−0.0531657	+	0.0920857i	0.838218	+	0.545336i	$0.183598\pi$
$830$	4.75198	+	5.06772i	0.164943	+	0.175903i
$831$	3.56123	+	6.16822i	0.123538	+	0.213973i
$832$	8.14552	−	41.7103i	0.282395	−	1.44605i
$833$	2.69938	−	1.68857i	0.0935279	−	0.0585054i
$834$	21.3575	+	6.46518i	0.739551	+	0.223871i
$835$	−6.58581	−	11.4070i	−0.227911	−	0.394754i
$836$	−18.5930	−	37.5927i	−0.643054	−	1.30017i
$837$	5.20192	+	3.00333i	0.179805	+	0.103810i
$838$	−16.3101	+	3.81298i	−0.563422	+	0.131717i
$839$	−39.0864			−1.34941			−0.674706	−	0.738087i	$-0.735730\pi$
$839$	−39.0864			−1.34941			−0.674706	+	0.738087i	$0.735730\pi$
$840$	−17.6552	−	6.25592i	−0.609162	−	0.215850i
$841$	22.3456			0.770536
$842$	30.0105	−	7.01586i	1.03423	−	0.241782i
$843$	−11.3069	−	6.52804i	−0.389430	−	0.224838i
$844$	7.40929	−	3.66458i	0.255038	−	0.126140i
$845$	19.0483	+	32.9926i	0.655281	+	1.13498i
$846$	−1.29628	−	0.392398i	−0.0445669	−	0.0134909i
$847$	27.2056	−	49.1081i	0.934795	−	1.68738i
$848$	−23.0686	+	9.61825i	−0.792179	+	0.330292i
$849$	−1.05685	−	1.83051i	−0.0362709	−	0.0628230i
$850$	−0.556624	−	0.593610i	−0.0190921	−	0.0203606i
$851$	−23.0820	+	39.9792i	−0.791241	+	1.37047i
$852$	−0.944674	+	14.6744i	−0.0323640	+	0.502737i
$853$	−26.4897			−0.906989			−0.453495	−	0.891259i	$-0.649823\pi$
$853$	−26.4897			−0.906989			−0.453495	+	0.891259i	$0.649823\pi$
$854$	−18.0122	−	5.10640i	−0.616364	−	0.174737i
$855$		−	9.24692i		−	0.316238i
$856$	−10.5723	+	28.2394i	−0.361355	+	0.965202i
$857$	38.9066	+	22.4627i	1.32902	+	0.767312i	0.985149	−	0.171703i	$-0.0549269\pi$
$857$	38.9066	+	22.4627i	1.32902	+	0.767312i	0.343875	+	0.939015i	$0.388260\pi$
$858$	29.1689	+	31.1070i	0.995808	+	1.06198i
$859$	30.6621	−	17.7028i	1.04618	−	0.604011i	0.124601	−	0.992207i	$-0.460235\pi$
$859$	30.6621	−	17.7028i	1.04618	−	0.604011i	0.921577	+	0.388196i	$0.126902\pi$
$860$	−15.2753	−	10.1810i	−0.520883	−	0.347168i
$861$	−12.3191	+	0.218004i	−0.419835	+	0.00742955i
$862$	−6.77677	+	22.3869i	−0.230818	+	0.762499i
$863$	2.40437	−	1.38816i	0.0818456	−	0.0472536i	−0.458519	−	0.888685i	$-0.651620\pi$
$863$	2.40437	−	1.38816i	0.0818456	−	0.0472536i	0.540364	+	0.841431i	$0.318286\pi$
$864$	2.31963	−	5.15939i	0.0789155	−	0.175526i
$865$	0.179745	−	0.311328i	0.00611151	−	0.0105855i
$866$	−54.0814	+	12.6432i	−1.83776	+	0.429632i
$867$		−	16.7931i		−	0.570324i
$868$	−28.2363	+	14.5929i	−0.958402	+	0.495314i
$869$			50.5915i			1.71620i
$870$	−2.07867	−	8.89156i	−0.0704737	−	0.301452i
$871$	−24.7092	+	42.7976i	−0.837239	+	1.45014i
$872$	1.48021	+	8.86922i	0.0501263	+	0.300350i
$873$	−3.21529	+	1.85635i	−0.108821	+	0.0628279i
$874$	25.6046	+	7.75082i	0.866089	+	0.262175i
$875$	12.7441	+	21.1982i	0.430830	+	0.716631i
$876$	−11.4060	−	7.60207i	−0.385373	−	0.256850i
$877$	−14.3264	+	8.27135i	−0.483768	+	0.279304i	−0.721986	−	0.691908i	$-0.756770\pi$
$877$	−14.3264	+	8.27135i	−0.483768	+	0.279304i	0.238217	+	0.971212i	$0.423437\pi$
$878$	−32.0144	+	30.0197i	−1.08043	+	1.01312i
$879$	0.289254	+	0.167001i	0.00975630	+	0.00563280i
$880$	34.4910	−	45.1667i	1.16269	−	1.52257i
$881$			24.6158i			0.829327i	0.909975	+	0.414664i	$0.136101\pi$
$881$			24.6158i			0.829327i	−0.909975	+	0.414664i	$0.863899\pi$
$882$	2.59320	+	9.55381i	0.0873176	+	0.321694i
$883$	40.4623			1.36167			0.680833	−	0.732439i	$-0.261618\pi$
$883$	40.4623			1.36167			0.680833	+	0.732439i	$0.261618\pi$
$884$	−4.82269	−	0.310463i	−0.162204	−	0.0104420i
$885$	12.6679	−	21.9415i	0.425827	−	0.737554i
$886$	0.871646	−	0.817338i	0.0292835	−	0.0274590i
$887$	4.64231	+	8.04072i	0.155873	+	0.269981i	0.933377	−	0.358898i	$-0.116847\pi$
$887$	4.64231	+	8.04072i	0.155873	+	0.269981i	−0.777503	+	0.628879i	$0.783514\pi$
$888$	−16.2115	−	19.6836i	−0.544021	−	0.660538i
$889$	−14.5065	+	8.72114i	−0.486532	+	0.292498i
$890$	7.00309	−	23.1345i	0.234744	−	0.775471i
$891$	2.83809	+	4.91572i	0.0950797	+	0.164683i
$892$	32.4595	−	16.0542i	1.08682	−	0.537535i
$893$	3.06399	+	1.76900i	0.102533	+	0.0591972i
$894$	1.91730	+	8.20130i	0.0641242	+	0.274293i
$895$	47.3688			1.58337
$896$	16.3563	+	25.0694i	0.546424	+	0.837509i
$897$	−27.2012			−0.908221
$898$	13.4386	+	57.4840i	0.448453	+	1.91827i
$899$	−13.4190	−	7.74746i	−0.447548	−	0.258392i
$900$	2.26786	−	1.12167i	0.0755953	−	0.0373888i
$901$	1.42106	+	2.46134i	0.0473423	+	0.0819993i
$902$	10.8308	−	35.7793i	0.360627	−	1.19132i
$903$	0.171664	+	9.70053i	0.00571262	+	0.322813i
$904$	−0.543843	−	0.660322i	−0.0180880	−	0.0219620i
$905$	27.8159	+	48.1786i	0.924632	+	1.60151i
$906$	3.70617	−	3.47526i	0.123129	−	0.115458i
$907$	−2.55327	+	4.42240i	−0.0847800	+	0.146843i	−0.905297	−	0.424778i	$-0.860352\pi$
$907$	−2.55327	+	4.42240i	−0.0847800	+	0.146843i	0.820517	+	0.571621i	$0.193685\pi$
$908$	−15.8177	−	1.01827i	−0.524928	−	0.0337925i
$909$	5.68155			0.188445
$910$	−47.8653	−	13.5697i	−1.58672	−	0.449830i
$911$		−	36.3702i		−	1.20500i	−0.798119	−	0.602500i	$-0.794171\pi$
$911$		−	36.3702i		−	1.20500i	0.798119	−	0.602500i	$-0.205829\pi$
$912$	−8.96856	+	11.7445i	−0.296979	+	0.388900i
$913$	9.64757	+	5.57003i	0.319288	+	0.184341i
$914$	7.72242	−	7.24127i	0.255435	−	0.239520i
$915$	10.8463	−	6.26211i	0.358567	−	0.207019i
$916$	−3.58764	−	2.39115i	−0.118539	−	0.0790059i
$917$	−33.5639	−	18.5942i	−1.10838	−	0.614034i
$918$	−0.615676	−	0.186372i	−0.0203203	−	0.00615121i
$919$	40.4248	−	23.3393i	1.33349	−	0.769892i	0.347659	−	0.937621i	$-0.386977\pi$
$919$	40.4248	−	23.3393i	1.33349	−	0.769892i	0.985833	+	0.167729i	$0.0536433\pi$
$920$	5.96742	+	35.7559i	0.196740	+	1.17884i
$921$	4.69571	−	8.13320i	0.154729	−	0.267998i
$922$	−1.39559	−	5.96964i	−0.0459612	−	0.196600i
$923$			39.0580i			1.28561i
$924$	−30.0030	−	1.39892i	−0.987025	−	0.0460211i
$925$		−	11.4052i		−	0.375000i
$926$	48.6386	−	11.3708i	1.59836	−	0.373666i
$927$	−2.95345	+	5.11553i	−0.0970042	+	0.168016i
$928$	−5.98378	+	13.3093i	−0.196427	+	0.436898i
$929$	33.8671	−	19.5532i	1.11114	−	0.641518i	0.172017	−	0.985094i	$-0.444972\pi$
$929$	33.8671	−	19.5532i	1.11114	−	0.641518i	0.939125	+	0.343576i	$0.111638\pi$
$930$	6.16029	−	20.3503i	0.202004	−	0.667314i
$931$	−0.914979	−	25.8441i	−0.0299872	−	0.847006i
$932$	−33.3086	−	22.2001i	−1.09106	−	0.727188i
$933$	13.7482	−	7.93750i	0.450095	−	0.259862i
$934$	−10.1559	−	10.8307i	−0.332310	−	0.354390i
$935$	−5.59661	−	3.23121i	−0.183029	−	0.105672i
$936$	5.26816	−	14.0716i	0.172195	−	0.459944i
$937$		−	14.4038i		−	0.470551i	−0.971929	−	0.235275i	$-0.924401\pi$
$937$		−	14.4038i		−	0.470551i	0.971929	−	0.235275i	$-0.0755992\pi$
$938$	−8.52210	−	33.7480i	−0.278256	−	1.10191i
$939$	−32.1656			−1.04969
$940$	−0.307990	+	4.78427i	−0.0100455	+	0.156046i
$941$	−13.1269	+	22.7364i	−0.427924	+	0.741186i	−0.996688	−	0.0813146i	$-0.974088\pi$
$941$	−13.1269	+	22.7364i	−0.427924	+	0.741186i	0.568765	+	0.822500i	$0.307421\pi$
$942$	0.951407	+	1.01462i	0.0309985	+	0.0330582i
$943$	11.9227	+	20.6508i	0.388257	+	0.672482i
$944$	−37.3704	+	15.5813i	−1.21630	+	0.507128i
$945$	−5.79280	−	3.20917i	−0.188440	−	0.104394i
$946$	−28.1739	−	8.52858i	−0.916014	−	0.277288i
$947$	−7.85354	−	13.6027i	−0.255206	−	0.442030i	0.709746	−	0.704458i	$-0.248810\pi$
$947$	−7.85354	−	13.6027i	−0.255206	−	0.442030i	−0.964951	+	0.262429i	$0.915477\pi$
$948$	15.9783	−	7.90276i	0.518953	−	0.256670i
$949$	−31.5306	−	18.2042i	−1.02353	−	0.590933i
$950$	−6.43576	+	1.50456i	−0.208804	+	0.0488142i
$951$	15.2712			0.495201
$952$	2.58874	−	2.21011i	0.0839015	−	0.0716302i
$953$	42.8466			1.38794			0.693968	−	0.720006i	$-0.255861\pi$
$953$	42.8466			1.38794			0.693968	+	0.720006i	$0.255861\pi$
$954$	−8.60451	+	2.01157i	−0.278581	+	0.0651268i
$955$	−25.5588	−	14.7564i	−0.827064	−	0.477506i
$956$	16.7511	+	33.8686i	0.541770	+	1.09539i
$957$	−7.32121	−	12.6807i	−0.236661	−	0.409909i
$958$	−22.9123	−	6.93583i	−0.740264	−	0.224087i
$959$	−3.25672	+	0.0576322i	−0.105165	+	0.00186104i
$960$	−19.6528	−	3.83795i	−0.634292	−	0.123869i
$961$	−2.53999	−	4.39939i	−0.0819352	−	0.141916i
$962$	−46.3297	−	49.4081i	−1.49373	−	1.59298i
$963$	−5.33045	+	9.23261i	−0.171771	+	0.297517i
$964$	36.5410	+	2.35235i	1.17691	+	0.0757641i
$965$	−67.1368			−2.16121
$966$	13.7417	−	13.3502i	0.442132	−	0.429537i
$967$		−	0.672082i		−	0.0216127i	−0.999942	−	0.0108063i	$-0.996560\pi$
$967$		−	0.672082i		−	0.0216127i	0.999942	−	0.0108063i	$-0.00343983\pi$
$968$	21.0429	−	56.2068i	0.676343	−	1.80655i
$969$	1.45526	+	0.840197i	0.0467498	+	0.0269910i
$970$	8.98945	+	9.58676i	0.288634	+	0.307812i
$971$	−6.45838	+	3.72875i	−0.207259	+	0.119661i	−0.600037	−	0.799972i	$-0.704847\pi$
$971$	−6.45838	+	3.72875i	−0.207259	+	0.119661i	0.392778	+	0.919633i	$0.371514\pi$
$972$	1.10921	−	1.66423i	0.0355778	−	0.0533802i
$973$	−35.7789	+	21.5099i	−1.14702	+	0.689575i
$974$	9.72184	−	32.1158i	0.311508	−	1.02906i
$975$	5.81991	−	3.36013i	0.186386	−	0.107610i
$976$	−19.8495	−	2.56628i	−0.635366	−	0.0821446i
$977$	−8.78701	+	15.2195i	−0.281121	+	0.486916i	−0.971661	−	0.236378i	$-0.924040\pi$
$977$	−8.78701	+	15.2195i	−0.281121	+	0.486916i	0.690540	+	0.723294i	$0.257373\pi$
$978$	−3.47255	+	0.811814i	−0.111040	+	0.0259589i
$979$		−	38.7596i		−	1.23876i
$980$	30.8409	−	16.6369i	0.985177	−	0.531446i
$981$			3.17911i			0.101501i
$982$	1.09843	+	4.69857i	0.0350525	+	0.149938i
$983$	−21.3661	+	37.0072i	−0.681472	+	1.18034i	0.293059	+	0.956094i	$0.405327\pi$
$983$	−21.3661	+	37.0072i	−0.681472	+	1.18034i	−0.974532	+	0.224250i	$0.928007\pi$
$984$	−12.9921	+	2.16829i	−0.414172	+	0.0691225i
$985$	−35.9489	+	20.7551i	−1.14543	+	0.661313i
$986$	1.58821	+	0.480770i	0.0505790	+	0.0153108i
$987$	2.17157	−	1.30552i	0.0691217	−	0.0415552i
$988$	−21.7685	+	32.6610i	−0.692548	+	1.03909i
$989$	16.2612	−	9.38839i	0.517075	−	0.298533i
$990$	14.6568	−	13.7436i	0.465824	−	0.436800i
$991$	39.3373	+	22.7114i	1.24959	+	0.721451i	0.971028	−	0.238967i	$-0.0768087\pi$
$991$	39.3373	+	22.7114i	1.24959	+	0.721451i	0.278563	+	0.960418i	$0.410142\pi$
$992$	−27.5619	+	19.8721i	−0.875091	+	0.630940i
$993$			21.0379i			0.667617i
$994$	−19.1695	−	19.7316i	−0.608020	−	0.625850i
$995$	28.5553			0.905264
$996$	0.252164	−	3.91708i	0.00799013	−	0.124117i
$997$	−21.8718	+	37.8831i	−0.692687	+	1.19977i	0.278268	+	0.960504i	$0.410240\pi$
$997$	−21.8718	+	37.8831i	−0.692687	+	1.19977i	−0.970954	+	0.239265i	$0.923094\pi$
$998$	18.0121	−	16.8898i	0.570162	−	0.534638i
$999$	−4.50782	−	7.80778i	−0.142621	−	0.247027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.t.a.115.8	yes	32
3.2	odd	2		504.2.bk.c.451.9		32
4.3	odd	2		672.2.bb.a.367.7		32
7.3	odd	6		1176.2.p.a.979.27		32
7.4	even	3		1176.2.p.a.979.28		32
7.5	odd	6	inner	168.2.t.a.19.4	✓	32
8.3	odd	2	inner	168.2.t.a.115.4	yes	32
8.5	even	2		672.2.bb.a.367.2		32
12.11	even	2		2016.2.bs.c.1711.4		32
21.5	even	6		504.2.bk.c.19.13		32
24.5	odd	2		2016.2.bs.c.1711.13		32
24.11	even	2		504.2.bk.c.451.13		32
28.3	even	6		4704.2.p.a.3919.1		32
28.11	odd	6		4704.2.p.a.3919.16		32
28.19	even	6		672.2.bb.a.271.2		32
56.3	even	6		1176.2.p.a.979.26		32
56.5	odd	6		672.2.bb.a.271.7		32
56.11	odd	6		1176.2.p.a.979.25		32
56.19	even	6	inner	168.2.t.a.19.8	yes	32
56.45	odd	6		4704.2.p.a.3919.15		32
56.53	even	6		4704.2.p.a.3919.2		32
84.47	odd	6		2016.2.bs.c.271.13		32
168.5	even	6		2016.2.bs.c.271.4		32
168.131	odd	6		504.2.bk.c.19.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.4	✓	32	7.5	odd	6	inner
168.2.t.a.19.8	yes	32	56.19	even	6	inner
168.2.t.a.115.4	yes	32	8.3	odd	2	inner
168.2.t.a.115.8	yes	32	1.1	even	1	trivial
504.2.bk.c.19.9		32	168.131	odd	6
504.2.bk.c.19.13		32	21.5	even	6
504.2.bk.c.451.9		32	3.2	odd	2
504.2.bk.c.451.13		32	24.11	even	2
672.2.bb.a.271.2		32	28.19	even	6
672.2.bb.a.271.7		32	56.5	odd	6
672.2.bb.a.367.2		32	8.5	even	2
672.2.bb.a.367.7		32	4.3	odd	2
1176.2.p.a.979.25		32	56.11	odd	6
1176.2.p.a.979.26		32	56.3	even	6
1176.2.p.a.979.27		32	7.3	odd	6
1176.2.p.a.979.28		32	7.4	even	3
2016.2.bs.c.271.4		32	168.5	even	6
2016.2.bs.c.271.13		32	84.47	odd	6
2016.2.bs.c.1711.4		32	12.11	even	2
2016.2.bs.c.1711.13		32	24.5	odd	2
4704.2.p.a.3919.1		32	28.3	even	6
4704.2.p.a.3919.2		32	56.53	even	6
4704.2.p.a.3919.15		32	56.45	odd	6
4704.2.p.a.3919.16		32	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.321935 - 1.37708i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.79272 + 0.886663i) q^{4} +(1.25150 + 2.16767i) q^{5} +(0.409738 - 1.35356i) q^{6} +(1.36321 + 2.26752i) q^{7} +(1.79815 + 2.18327i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.58215 - 2.42127i) q^{10} +(2.83809 - 4.91572i) q^{11} +(-1.99587 - 0.128485i) q^{12} -5.31228 q^{13} +(2.68370 - 2.60725i) q^{14} +2.50301i q^{15} +(2.42766 - 3.17907i) q^{16} +(-0.393919 - 0.227429i) q^{17} +(1.03162 - 0.967346i) q^{18} +(-3.19938 + 1.84716i) q^{19} +(-4.16558 - 2.77635i) q^{20} +(0.0468128 + 2.64534i) q^{21} +(-7.68304 - 2.32575i) q^{22} +(4.43443 - 2.56022i) q^{23} +(0.465606 + 2.78984i) q^{24} +(-0.632521 + 1.09556i) q^{25} +(1.71021 + 7.31545i) q^{26} +1.00000i q^{27} +(-4.45438 - 2.85632i) q^{28} -2.57962i q^{29} +(3.44685 - 0.805806i) q^{30} +(3.00333 - 5.20192i) q^{31} +(-5.15939 - 2.31963i) q^{32} +(4.91572 - 2.83809i) q^{33} +(-0.186372 + 0.615676i) q^{34} +(-3.20917 + 5.79280i) q^{35} +(-1.66423 - 1.10921i) q^{36} +(-7.80778 + 4.50782i) q^{37} +(3.57369 + 3.81115i) q^{38} +(-4.60057 - 2.65614i) q^{39} +(-2.48222 + 6.63015i) q^{40} +4.65692i q^{41} +(3.62778 - 0.916092i) q^{42} +3.66703 q^{43} +(-0.729306 + 11.3289i) q^{44} +(-1.25150 + 2.16767i) q^{45} +(-4.95323 - 5.28235i) q^{46} +(-0.478841 - 0.829377i) q^{47} +(3.69195 - 1.53933i) q^{48} +(-3.28332 + 6.18222i) q^{49} +(1.71230 + 0.518335i) q^{50} +(-0.227429 - 0.393919i) q^{51} +(9.52341 - 4.71020i) q^{52} +(-5.41124 - 3.12418i) q^{53} +(1.37708 - 0.321935i) q^{54} +14.2075 q^{55} +(-2.49936 + 7.05359i) q^{56} -3.69433 q^{57} +(-3.55235 + 0.830471i) q^{58} +(-8.76604 - 5.06108i) q^{59} +(-2.21932 - 4.48718i) q^{60} +(-2.50184 - 4.33331i) q^{61} +(-8.13036 - 2.46115i) q^{62} +(-1.28213 + 2.31434i) q^{63} +(-1.53334 + 7.85168i) q^{64} +(-6.64834 - 11.5153i) q^{65} +(-5.49083 - 5.85568i) q^{66} +(4.65133 - 8.05634i) q^{67} +(0.907837 + 0.0584425i) q^{68} +5.12043 q^{69} +(9.01031 + 2.55439i) q^{70} -7.35240i q^{71} +(-0.991694 + 2.64888i) q^{72} +(5.93541 + 3.42681i) q^{73} +(8.72125 + 9.30073i) q^{74} +(-1.09556 + 0.632521i) q^{75} +(4.09777 - 6.14821i) q^{76} +(15.0154 - 0.265718i) q^{77} +(-2.17664 + 7.19047i) q^{78} +(-7.71882 + 4.45646i) q^{79} +(9.92938 + 1.28374i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.41297 - 1.49923i) q^{82} +1.96259i q^{83} +(-2.42944 - 4.70083i) q^{84} -1.13851i q^{85} +(-1.18055 - 5.04980i) q^{86} +(1.28981 - 2.23402i) q^{87} +(15.8357 - 2.64286i) q^{88} +(5.91361 - 3.41423i) q^{89} +(3.38796 + 1.02558i) q^{90} +(-7.24175 - 12.0457i) q^{91} +(-5.67961 + 8.52158i) q^{92} +(5.20192 - 3.00333i) q^{93} +(-0.987965 + 0.926409i) q^{94} +(-8.00807 - 4.62346i) q^{95} +(-3.30835 - 4.58856i) q^{96} +3.71270i q^{97} +(9.57044 + 2.53113i) q^{98} +5.67619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more